# Quantum field heat engine powered by phonon-photon interactions

Alessandro Ferreri ID Institute for Quantum Computing Analytics (PGI-12),
Forschungszentrum Jülich, 52425 Jülich, Germany  Theoretical Quantum Physics
Laboratory, RIKEN, Wako-shi, Saitama 351-0198, Japan  Vincenzo Macrì ID
Theoretical Quantum Physics Laboratory, RIKEN, Wako-shi, Saitama 351-0198,
Japan  Dipartimento di Ingegneria, Università degli Studi di Palermo, Viale
delle Scienze, 90128 Palermo, Italy  Frank K. Wilhelm ID Institute for Quantum
Computing Analytics (PGI-12), Forschungszentrum Jülich, 52425 Jülich, Germany
Franco Nori ID Theoretical Quantum Physics Laboratory, RIKEN, Wako-shi,
Saitama 351-0198, Japan  Center for Quantum Computing, RIKEN, Wako-shi,
Saitama 351-0198, Japan  Physics Department, The University of Michigan, Ann
Arbor, Michigan 48109-1040, USA  David Edward Bruschi ID Institute for Quantum
Computing Analytics (PGI-12), Forschungszentrum Jülich, 52425 Jülich, Germany

###### Abstract

We present a quantum heat engine based on a cavity with two oscillating
mirrors that confine a quantum field as the working substance. The engine
performs an Otto cycle during which the walls and a field mode interact via a
nonlinear Hamiltonian. Resonances between the frequencies of the cavity mode
and the walls allow to transfer heat from the hot and the cold bath by
exploiting the conversion between phononic and photonic excitations. We study
the time evolution of the system and show that net work can be extracted after
a full cycle. We evaluate the efficiency of the process.

_Introduction._ — Quantum thermodynamics studies physical processes at the
quantum scale through the lens of thermodynamics [1, 2, 3]. The overall aim of
this field of research is to extend concepts initially developed in the
classical theory, such as heat, work and thermodynamic efficiency, into the
quantum domain where purely quantum features can be exploited [4, 5]. These
include quantum correlations [6], quantum coherence [7] and vacuum
fluctuations [8, 9]. One task is to propose and characterize novel
thermodynamic cycles by taking advantage of the nonclassical nature of the
working substance to extract work for different tasks [10, 11]. The interest
in studying thermodynamical cycles at the quantum level goes beyond the mere
possibility of reaching higher degrees of efficiency but aims towards
miniaturization of future thermal machines based on quantum systems.

The quantum Otto cycle is a thermodynamic cycle that enjoys relative ease of
theoretical implementation in a quantum framework compared to other cycles,
especially if implemented in cavity-optomechanics [12, 13, 14, 15, 16, 17]. It
consists of a combination of two thermodynamic “strokes”: i) the isochoric
transformation, performed by maintaining constant the spacing of the energy
levels of the system during thermalization with the bath; ii) the adiabatic
transformation, where the thermally isolated system evolves with the number of
excitations kept constant. This simple cycle has been implemented and studied
in the context of finite-time Otto cycles [18, 19, 20], Otto-engine power
generation [21, 22, 23], heat engines with interacting systems [24], and
quantum heat engines based on phononic fields in Bose-Einstein condensates
[25].

In this work we study the quantum Otto cycle in the context of quantum
optomechanics [26]. The system consists of a cavity-optomechanical setup where
two movable mirrors confine a quantum field. The mirror and field modes
strongly interact via phonon-photon vacuum fluctuations, and the mirrors are
also coupled individually to a thermal bath. We employ our system to show that
the proposed quantum field heat engine can generate power in finite time after
each cycle, and we estimate the efficiency of such process. We note that the
platforms considered here have already allowed for the experimental
observation of thermal-phonon hopping, i.e, the exchange of thermal energy
between individual phonon modes [27].

In contrast to the standard quantum Otto cycle, the cavity mode here plays the
role of working substance and does not interact with the baths directly.
Instead, the interaction is mediated by the quantized position degree of
freedom of the respective wall. More precisely, each wall is connected to a
thermal bath: the first wall (called W1) interacts with a cold bath at
temperature $T_{\textrm{c}}$, while the second wall (called W2) interacts with
a hot bath at temperature $T_{\textrm{h}}$. The transfer of thermal
excitations from the bath to the cavity mode occurs whenever the frequency of
the cavity is resonant with the frequency of the corresponding wall. The field
modes are driven by an external drive, which controls the length of the
cavity.

We stress that the photon-phonon interaction occurs beyond linearization,
thereby retaining the dynamical-Casimir-like three-body terms in the
Hamiltonian [28, 29, 30, 31, 32, 33], with the ambition of characterizing the
thermodynamic performance of the system in its full nonlinear regime. This
includes also the multimode character of the interaction [34]. Moreover, in
contrast to standard studies of four-stroke thermal machines that consider the
single strokes separately, we employed the master equation formalism in order
to run two consecutive cycles as a function of time. The need for the master
equation approach throughout the whole dynamics is explained by the fact that
we effectively change the length of the cavity in a time-dependent way through
the external drive, thereby controlling the heat transfer between the cavity
and the baths through the walls.

_The quantum model._ — The system is composed of two movable walls that
confine an uncharged massless scalar quantum field and interact with a local
bath. Our choice of field is a good approximation for a single-polarization
version of a confined electromagnetic spin-1 field [35]. We further simplify
the setup by considering a one dimensional cavity, which allows us to obtain
the system Hamiltonian $\hat{H}_{s}$ following the standard procedure of
solving the classical field equations and then quantizing [31]. The system is
schematically represented in Fig.1.

Figure 1: Pictorial representation of the cavity performing the quantum Otto
cycle: two movable walls, coupled to two baths at different temperatures,
confine a cavity mode, which is weakly coupled to a bath at $T\simeq 0$. The
four panels describe the four strokes of the cycle: (a) cold isochoric, (b)
adiabatic compression, (c) hot isochoric, (d) adiabatic expansion.

The Hamiltonian can be split as usual as
$\hat{H}_{\textrm{s}}=\hat{H}_{0}+\hat{H}_{\textrm{I}}$, where
$\hat{H}_{0}=\omega_{1}\hat{b}_{1}^{\dagger}\hat{b}_{1}+\omega_{2}\hat{b}_{2}^{\dagger}\hat{b}_{2}+\omega_{\textrm{c}}\hat{a}^{\dagger}\hat{a}$
is the bare Hamiltonian and $H_{I}$ is the interaction Hamiltonian. The latter
has been previously obtained [26], and reads

$\displaystyle\hat{H}_{\textrm{I}}=$
$\displaystyle\frac{g_{1}}{2}(\hat{a}+\hat{a}^{\dagger})^{2}(\hat{b}_{1}+\hat{b}_{1}^{\dagger})+\frac{g_{2}}{2}(\hat{a}+\hat{a}^{\dagger})^{2}(\hat{b}_{2}+\hat{b}_{2}^{\dagger}).$
(1)

Here, $\hat{a},\hat{a}^{\dagger}$ are the photonic operators for the cavity-
field mode, while $\hat{b}_{j},\hat{b}^{\dagger}_{j}$ ($j=1,2$) are the
phononic operators for the walls-field mode. The operators satisfy the
canonical commutator relations $[\hat{a},\hat{a}^{\dagger}]=1$ and
$[\hat{b}_{j},\hat{b}^{\dagger}_{j^{\prime}}]=\delta_{jj^{\prime}}$.
Furthermore, $\omega_{j}$ are the frequencies of the two movable walls
($\omega_{1}<\omega_{2}$ for convenience), whereas $\omega_{\textrm{c}}$ is
the frequency of the cavity field mode. In addition, the coupling constants
$g_{j}$ quantify the strength of the coupling between the field mode and the
$j$th-wall (see Appendix). Finally, eigenvalues and states will be labelled by
$l,m,n\in\mathbb{N}$, which stand for $l$ excitations of the field mode, $m$
excitations of W1 and excitations $n$ of W2. Throughout this work we assume
that $\hbar=c=k_{B}=1$.

The interaction Hamiltonian Eq. (1) contains three types of terms: (i) The
radiation pressure
$\hat{a}^{\dagger}\hat{a}(\hat{b}_{j}+\hat{b}_{j}^{\dagger})$, paramount in
standard optomechanics [36, 37], which shifts the cavity frequency
$\omega_{\textrm{c}}$ in case of coherent motion of the wall. (ii) The
excitation transfer terms
$\hat{a}^{2}\hat{b}_{j}^{\dagger}+(\hat{a}^{\dagger})^{2}\hat{b}_{j}$, which
convert single-phonon excitations into photon pairs (and vice versa). In other
words, they convert mechanical and electromagnetic energy into each other. In
order for the photons to appear and contribute during the dynamics, resonance
conditions $k\omega_{j}=2\omega_{\textrm{c}}$ with $k\in\mathbb{N}$ involving
high-frequency movable walls must be fulfilled [30]. Such resonances can be
achieved in current optomechanical setups using real movable mirrors [38].
However, they play the most significant role in experimental platforms based
on superconducting circuits [39, 40, 41, 42]. (iii) The counter-rotating terms
$\hat{a}^{2}\hat{b}_{j}+(\hat{a}^{\dagger})^{2}\hat{b}_{j}^{\dagger}$, which
generally contribute to modifying the energy-density of the cavity field
(because of the quantum wall fluctuations [29]) and are also responsible for
the non-conservation of the particle number. Counter-rotating terms are
involved in virtual processes that would allow to observe higher-order
coherent processes in cavity-optomechanics [43, 44].

The interaction between the bosonic modes not only inevitably alters the
structure of the energy levels with respect to the bare ones, but it also
lifts the degeneracy in the presence of resonances. To this end we diagonalize
the Hamiltonian $H_{\textrm{s}}$ numerically and plot the energy levels in
Fig. 2 for different values of the frequency $\omega_{\textrm{c}}$. The figure
clearly shows the presence of avoided level crossings due to the energy split
in proximity of the frequency values $\omega_{\textrm{c},1}=\omega_{1}/2$ and
$\omega_{\textrm{c},2}=\omega_{2}/2$, i.e., where the resonances are expected
to occur as discussed above. The dashed vertical lines in Fig. 2 highlight the
shift in the bare frequencies. The effective cavity-frequencies
$\tilde{\omega}_{\textrm{c},i}$ ($i=1,2$) involved in the coherent resonant
processes can be estimated numerically by calculating the minimal splitting of
the avoided level crossings.

Figure 2: Lowest-energy levels of the system Hamiltonian as a function of
$\omega_{\textrm{c}}$. Circles highlight the avoided levels in which the
dressed resonances (blue) $\omega_{1}=2\omega_{\textrm{c},1}$ and (red)
$\omega_{2}=2\omega_{\textrm{c},2}$ occur. For each resonance condition, the
effective cavity frequency $\tilde{\omega}_{\textrm{c}}$ was estimated. Here:
$\tilde{\omega}_{\textrm{c},1}=1.01$, $\tilde{\omega}_{\textrm{c},2}=1.31$,
$\omega_{1}=2$, $\omega_{2}=2.6$, $g_{1}=g_{2}=0.05$. Frequencies are
normalized with respect to the bare frequency of the cavity mode
$\omega_{\textrm{c},1}$.

We use open quantum system dynamics to compute all quantities of interest
[45]. This requires us to solve the master equation for the density operator
$\hat{\rho}$ representing the state. Since we are considering a strongly
interacting system, we employ the tools developed in the literature [46, 47,
31]. In particular, we employ the Lindblad equation
$\dot{\hat{\rho}}=-i[\hat{H},\hat{\rho}]+{\hat{\mathcal{L}}_{\rm
D}}\hat{\rho}$, where ${\hat{\mathcal{L}}_{\rm D}}$ indicates the Lindblad
superoperator expressed in the dressed base (see Appendix). Here we assume
that the three subsystems are coupled to three different baths: W1 is coupled
to a cold bath with damping rate $\gamma_{1}$ and temperature
$T_{\textrm{c}}$; W2 is coupled to a hot bath with damping rate $\gamma_{2}$
and temperature $T_{\textrm{h}}$; the cavity mode interacts with its own bath
with damping rate $\kappa\simeq 0$ temperature $T\simeq 0$. This is a
reasonable assumption for realistic implementations.

_Quantum Otto cycle._ —The main idea of this work is to perform the quantum
Otto cycle by using the two walls as bosonic channels to perform the heat
transfer between the hot and cold baths through the cavity mode by exploiting
the mechanical-electromagnetic energy conversion. We present here the
framework employed to achieve our goal.

Any heat engine can be characterized by evaluating the output power
$\mathcal{P}$ and the efficiency $\eta$ of a single thermodynamic cycle. Thus,
we consider the total Hamiltonian
$\hat{H}_{\textrm{tot}}(t)=\hat{H}_{\textrm{s}}+\hat{H}_{\textrm{dr}}(t)$ that
includes the time-dependent drive term $\hat{H}_{\textrm{dr}}(t)$. This
contribution is expressed in the dressed picture and periodically drives the
cavity frequency from $\tilde{\omega}_{\textrm{c},1}$ to
$\tilde{\omega}_{\textrm{c},2}$ and vice versa, simulating the physical
process of compression and expansion of the cavity. This can be understood
from the fact that the frequency of a trapped field mode decreases or
increases by respectively enhancing or reducing the length of the cavity.
Thus, changes in frequency simulate changes in length. Concretely, we have
$\hat{H}_{\textrm{dr}}(t)=f(t)\Delta\omega\hat{A}^{\dagger}\hat{A}$, where
$\Delta\omega=\tilde{\omega}_{\textrm{c},2}-\tilde{\omega}_{\textrm{c},1}$,
$\hat{A},\hat{A}^{\dagger}$ are the cavity dressed operators obtained by
diagonalizing the Hamiltonian, and $f(t)$ is a periodic smooth step function
(see Appendix). Such step functions are commonly employed in circuit quantum
electrodynamics (QED) [48, 49, 50, 51, 52, 53]. Furthermore, time dependent
drives have also been considered in studies of nonlinear optomechanics [54,
55, 56].

In order to investigate the thermodynamic features of the system, we define
the change of internal energy
$\Delta\mathcal{U}(t)=\textrm{Tr}[\hat{H}_{\textrm{tot}}(t)\rho(t)]-\textrm{Tr}[\hat{H}_{\textrm{tot}}(0)\rho(0)]$,
the change in heat
$\Delta\mathcal{Q}(t)=\int_{0}^{t}d\tau\,\textrm{Tr}\bigl{[}\hat{H}_{\textrm{tot}}(\tau)\dot{\rho}(\tau)\bigr{]}$,
and the change in work
$\Delta\mathcal{W}(t)=\int_{0}^{t}d\tau\,\textrm{Tr}\left[\dot{\hat{H}}_{\textrm{tot}}(\tau)\rho(\tau)\right]$.
These three quantities satisfy the first law of thermodynamics in its quantum
formulation:

$\displaystyle\Delta\mathcal{U}(t)=\Delta\mathcal{Q}(t)+\Delta\mathcal{W}(t).$
(2)

We then provide a formal definition for the output power $\mathcal{P}$ and the
efficiency $\eta$ of a thermodynamical process as

$\displaystyle\mathcal{P}:=\frac{d}{dt}\Delta\mathcal{W}(t),\quad\eta:=-\frac{\mathcal{W}^{\textrm{out}}}{\mathcal{Q}^{\textrm{in}}},$
(3)

where $\mathcal{W}^{\textrm{out}}$ and $\mathcal{Q}^{\textrm{in}}$ are,
respectively, the work provided and the heat absorbed by the system. These are
the main expressions evaluated in our work.

We now present our quantum Otto cycle, which is composed of a preliminary
phase and four steps: (0) Initialization: the whole system is prepared in its
vacuum state $\rho(0)=\lvert 0\rangle\langle 0\rvert$ and we assume that the
cavity is initially coupled to W1 by means of the resonance condition
$\omega_{\textrm{c},1}=\omega_{1}/2$ (see Fig. 1); (a)  Cold isochoric:
Thermal cold phonons from W1 are converted into photons, until the subsystem
W1+cavity is thermalized; (b) Adiabatic compression: The external drive shifts
the field frequency from $\tilde{\omega}_{\textrm{c},1}$ to
$\tilde{\omega}_{\textrm{c},2}$ ; (c)  Hot isochoric: The newly activated
resonance $\omega_{\textrm{c}2}=\omega_{2}/2$ facilitates the excitation
transfer between the cavity mode and W2, during which hot phonons are
converted into photons; (d)  Adiabatic expansion: The drive changes the cavity
mode frequency back to the resonance regime
$\omega_{\textrm{c},1}=\omega_{1}/2$. After this step, the system is ready to
restart from the cold isochoric stroke of step (a).

We now offer a few remarks on the properties of our cycle and the differences
with the standard quantum Otto cycle already known in the literature [10].
Recall that a quantum isochoric transformation occurs whenever the population
of the system changes while thermalizing with a bath and maintaining the
energy level spacing constant, while a quantum adiabatic transformation occurs
whenever both the energy level spacing and the temperature are tuned such that
the population does not vary throughout the process [57, 10]. The requirements
for a transformation to be called “quantum adiabatic” dramatically differ with
respect to the classical case. Indeed, while a classical adiabatic
transformation simply forces the system to be thermally isolated throughout
the process, namely not coupled to any bath, the condition of quantum
adiabaticity additionally requires the stability of the population [10]. In
this sense, the latter is conceptually more limiting and challenging to
realize in an experiment. Furthermore, any quantum adiabatic transformation
has to be performed very slowly, namely without generating any output power
[21, 22, 58].

Importantly, since the frequency change occurs much faster than the effective
coupling, the system does not have time to modify its eigenstates, which
implies that we do not need to diagonalize the Hamiltonian at all times.
Therefore, we can maintain the same eigenbasis, hence the same dressed
operators, throughout the whole dynamics. Moreover, the interaction between
the cavity and each wall occurs not only at the minimum point of the level
avoidance but also weakly in its proximity. It follows that this rapid jump
between $\tilde{\omega}_{\textrm{c},1}$ and $\tilde{\omega}_{\textrm{c},2}$ is
necessary to ensure the classical adiabaticity of the process [10], namely
simulating the deactivation of the interaction between the cavity and the bath
mediated by the wall. In this quantum description, the two walls are
thermalized via different baths. In particular, the interaction between a
specific bath and the cavity occurs once the resonance condition with the
relative wall is imposed, and it is halted once the system is driven off-
resonance. We have W2 at frequency $\omega_{2}$ that thermalizes via a hot
bath at $T_{\textrm{h}}$, while W1 has a lower frequency
$\omega_{1}<\omega_{2}$ and it is thermalized via a cold bath at
$T_{\textrm{c}}<T_{\textrm{h}}$. The cavity interacts with its own bath at
$T\simeq 0$.

_Numerical analysis._ — We have solved numerically the master equation and
therefore calculated the time evolution of the average internal energy
$\Delta\mathcal{U}(t)$ directly, while we have computed the average work
$\Delta\mathcal{W}(t)$ by integrating the expression of the power
$\mathcal{P}(t)\equiv\textrm{Tr}[\rho(t)\dot{H}_{\textrm{tot}}(t)]=\textrm{Tr}[\rho(t)\dot{H}_{\textrm{dr}}(t)]=\dot{f}(t)\Delta\omega\textrm{Tr}[\rho(t)\hat{A}^{\dagger}\hat{A}]$
defined in Eq. (3). The average heat change $\Delta\mathcal{Q}(t)$ can be
easily derived employing the first law of thermodinamics in Eq. (2). We have
used the parameters indicated in Fig. 3, and our choice of frequencies has
followed two important criteria: we need to clearly distinguish the two
avoided levels in order to perform the jump, but at the same time we must
avoid any degeneracy with other possible resonances in order to prevent
unwanted heat flows that could reduce the efficiency. Our results can be found
in Fig. 3.

We now discuss our findings. Once the dynamics start, a transient phase occurs
in which both walls absorb thermal excitations from their own baths. However,
while the interaction between W1 and the cavity converts part of the thermal
phonons into photons, W2, which is momentarily not interacting with the
cavity, thermalizes. In Fig. 3a, $\Delta\mathcal{U}=0$ corresponds to the
energy of the system at the end of this transient phase. Recall that
thermalization of the cavity while interacting with W1 is defined as stroke
(a). During stroke (b), i.e., during compression, the cavity absorbs work from
the drive and increases $\tilde{\omega}_{\textrm{c},1}$ to
$\tilde{\omega}_{\textrm{c},2}$, eventually starting to absorb thermal
excitations from the hot wall and converting them into photons [which defines
stroke (c)]. This causes a drastic enhancement of the photon population at the
expense of part of the phonon population, as seen in Fig. 3b. At the same
time, the population of the cold wall, now off-resonance, increases and W1
thermalizes completely. Once the internal energy becomes constant and the
populations stop fluctuating, we perform the rapid expansion of the cavity as
described in stroke (d), which causes the system to release an amount of
energy which is higher than the one initially absorbed, a key feature of a
properly functioning heat engine. This net gain becomes evident by looking at
$\Delta\mathcal{W}$ in Fig. 3a. After this last stroke, the cavity thermalizes
with W1 again and the system reaches its initial configuration: a new cycle
can now take place. We conclude that, after each cycle, we can extract a net
amount of work using our system.

Figure 3: Time evolution of the quantities of interest. (a): variation of
internal energy $\Delta\mathcal{U}$ (dashed, black), the work $\mathcal{W}$
(blue), and the heat $\mathcal{Q}$ (red). (b): population of the cavity photon
(black), the cold wall 1 phonons (dashed green) and the hot wall 2 phonons
(dashed red). The background colors indicate the four stokes shown in Fig. 1:
cold isochoric (orange), adiabatic compression (green), hot isochoric (red),
adiabatic expansion (blue). Here: $\omega_{1}=2$, $\omega_{2}=2.6$,
$\tilde{\omega}_{\textrm{c},1}=1.01$, $\tilde{\omega}_{\textrm{c},2}=1.31$,
$g_{1}=g_{2}=0.05$, $T_{\textrm{c}}=0.15$, $T_{\textrm{h}}=0.40$,
$\gamma_{1}=\gamma_{2}=\gamma=0.01$, $\kappa=10^{-6}$, $T_{0}=10^{-7}$.
Frequencies and temperatures are normalized with respect to
$\omega_{\textrm{c},1}$.

At this point, we wish to provide a measure of quality for the proposed cycle.
This can be done by means of the efficiency defined in Eq. (3), which we
compute using the parameters employed in the figures. We find an efficiency of
$\eta$=0.376, which can be compared to the Carnot limit
$\eta_{C}=1-T_{\textrm{c}}/T_{\textrm{h}}$=0.625 as a benchmark for the
performance of the machine. Further benchmarking could be carried out by
evaluating the efficiency at maximum power [58]. Such analysis would require a
detailed numerical optimization of this efficiency as a function of the
frequencies of the two walls, and it could include the activation of further
resonances during the adiabatic transformations. This is beyond the scope of
the present work, and it is left for future investigations.

We now provide a few remarks on our proposal. As mentioned before we note
that, once the resonance with the wall $j$ is implemented, the interaction
between wall $j$ and the cavity mode is given by terms
$(\hat{a}^{\dagger})^{2}\hat{b}_{j}+\hat{a}^{2}\hat{b}_{j}^{\dagger}$ in
$\hat{H}_{\textrm{I}}$, which mediate the phonon-photon conversions. From a
physical point of view this means that the degree of freedom that thermalizes
during any isochoric stroke is not the cavity mode alone, but is instead the
combination of the cavity mode and the activated wall. In other words, during
the isochoric transformation the change in photon population is not a direct
consequence of the thermalization of the cavity mode with the relative bath,
instead it is a consequence of the partial conversion of thermal phonons into
photon pairs. This process continues until the system wall-cavity reaches the
steady state, as can be observed in Fig. 3b. Thus, the number of photons at
the end of any isochoric process will be less than
$N=(e^{\omega_{\textrm{c}}/T_{0}}-1)^{-1}$ as predicted by Bose-Einstein
statistics and expected in the Otto cycle with a single-mode as working
substance [59, 60]. In particular, the photon population in Fig.3b can be
compared with the average number of photons for a single cavity mode with
frequency $\tilde{\omega}_{\textrm{c},1}=1.01$ and temperature
$T_{\textrm{c}}=0.15$, which is $N=1.2\cdot 10^{-3}$, and the population of a
single-cavity mode with frequency $\tilde{\omega}_{\textrm{c},2}=1.31$ and
temperature $T_{\textrm{h}}=0.4$, which is $N=3.96\cdot 10^{-2}$. It can be
seen that the photon population in our system is about 94% less than what
expected by a direct thermalization with the bath at the end of the cold
isochoric, and about 95% less at the end of the hot isochoric. This suggests
that we can run our machine with fewer resources.

Furthermore, we notice that, during the isochoric strokes, quantum excitations
are extracted from the thermal fluctuations of the walls and converted into
photons without requiring the walls to perform any classical motion. This is
in contrast to the semiclassical description of our setup, wherein walls are
treated as classical degrees of freedom [33]. The phonon-photon conversion
occurs between two quantum channels by simply activating the resonance
$\omega_{i}=2\omega_{\textrm{c},i}$ ($i=1,2$). The possibility of extracting
thermal excitations from the walls in case of no coherent motion is a
consequence of the fact that the two mirrors operate in the quantum regime
[61, 31].

Finally, we stress that, in contrast to other works studying optomechanical
systems in a quantum thermodynamic framework [12, 13], we employ a nonlinear
Hamiltonian that includes the nonlinear interaction between the movable walls
and the electromagnetic mode. In particular, the entire dynamics of our system
is based on the conversion of phonons into photons and vice versa. To our
knowledge, this effect has never been considered in a quantum thermodynamic
context. This highlights the importance of moving beyond the linearized
regime.

_Conclusions._ —In this work we proposed a quantum heat engine based on a
cavity system composed of a scalar field trapped by two fluctuating walls that
performs an Otto cycle. In our setup, we exploit the phonon-photon conversion
mechanism to let the working substance, namely the cavity mode, exchange heat
with the thermal baths during the cycle. We demonstrated that it is possible
to extract net work using carefully modulated resonances, and we have
evaluated the overall efficiency of the cycle. We believe that this work opens
the way to the systematic study of quantum field thermodynamic engines, to be
used for fundamental science, as well as the development of novel quantum
technologies.

_Acknowledgments._ —A.F. thanks the research center RIKEN for the hospitality.
A.F. acknowledges the “JSPS Summer Program 2022” and the “FY2022 JSPS
Postdoctoral Fellowship for Research in Japan (Short-term)”, sponsored by the
Japanese Society for the Promotion of Science (JSPS). F.K.W., A.F., and D.E.B.
acknowledge support from the joint project No. 13N15685 “German Quantum
Computer based on Superconducting Qubits (GeQCoS)” sponsored by the German
Federal Ministry of Education and Research (BMBF) under the framework “Quantum
technologies–from basic research to the market”. F.N. is supported in part by:
Nippon Telegraph and Telephone Corporation (NTT) Research, the Japan Science
and Technology Agency (JST) [via the Quantum Leap Flagship Program (Q-LEAP),
and the Moonshot R&D Grant Number JPMJMS2061], the Asian Office of Aerospace
Research and Development (AOARD) (via Grant No. FA2386-20-1-4069), and the
Foundational Questions Institute Fund (FQXi) via Grant No. FQXi-IAF19-06.

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##  Appendix A Derivation of the Hamiltonian

The literature shows different ways to derive the Hamiltonian of the system. A
possible starting point could be the classical equation of motion of both the
cavity and the two walls using time-dependent boundary conditions, as done by
Law in [28]. However, in this section we show how to derive the Hamiltonian of
the system from first principles employing the protocol in [31]. This
procedure is based on the idea that the position of a non-fixed wall undergoes
a fluctuation described by a quantum harmonic oscillator. This concept avoids
the treatment of the problem starting from dynamical equations, since a real
(classical) motion of the wall would occur only in presence of coherence.

We start from the Lagrangian density of a massless scalar field in
(3+1)-dimension:

$\displaystyle\mathcal{L}(t,\mathbb{x})=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi.$
(4)

The equation of motion of such Lagrangian density with static Dirichlet
boundary conditions is the Klein Gordon equation
$\partial_{t}^{2}\phi-\nabla^{2}\phi$=0, which can be solved by any scalar
field of the form

$\displaystyle\phi(t,\mathbb{x})=$
$\displaystyle\sum_{\mathbb{n}}\left[\alpha_{\mathbb{n}}\,\phi_{\mathbb{n}}(t,x)+\alpha_{\mathbb{n}}^{*}\,\phi^{*}_{\mathbb{n}}(t,x)\right],$
(5)

with modes

$\displaystyle\phi_{\mathbb{n}}(t,\mathbb{x})=$
$\displaystyle\sqrt{\frac{4}{\omega_{\mathbb{n}}V}}e^{-i\omega_{\mathbb{n}}t}\sin\left(\frac{n_{x}\pi}{L_{x}}x\right)\sin\left(\frac{n_{y}\pi}{L_{y}}y\right)\sin\left(\frac{n_{z}\pi}{L_{z}}z\right),$
(6)

where the dispersion law reads

$\displaystyle\omega_{\mathbb{n}}:=\sqrt{\left(\frac{n_{x}\pi}{L_{x}}\right)^{2}+\left(\frac{n_{y}\pi}{L_{y}}\right)^{2}+\left(\frac{n_{z}\pi}{L_{z}}\right)^{2}},$
(7)

with $\mathbb{n}\equiv(n_{x},n_{y},n_{y})$ a set of positive integer numbers,
and box having volume $V=L_{x}L_{y}L_{z}$ [62]. With the typical formalism,
well-known from field theory, we can calculate the Hamiltonian density
$\mathcal{H}(t,\mathbb{x})=\frac{1}{2}\left[\Pi^{2}(t,\mathbb{x})+(\nabla\phi(t,\mathbb{x}))^{2}\right]$,
with canonical momentum $\Pi(t,\mathbb{x}):=-\partial_{t}\phi(t,\mathbb{x})$.

Hence, the protocol consists in four steps:

  * i)

Extension of the box length with respect to $L_{x}$: $L_{x}\rightarrow
L_{x}+\Delta L_{x}$, where $\Delta L_{x}/L_{x}\ll 1$, and Taylor-expansion of
$\mathcal{H}(t,\mathbb{x})$ up to the first order in $\Delta L_{x}/L_{x}$;

  * ii)

Spatial integration of the Hamiltonian density in volume $V$, thereby
obtaining the classical Hamiltonian $H:=\int\mathcal{H}\,dV$;

  * iii)

Quantization of the field Fourier coefficients $\alpha_{\mathbb{n}}$:

$\displaystyle\alpha_{\mathbb{n}}\rightarrow$
$\displaystyle\hat{a}_{\mathbb{n}},$
$\displaystyle\alpha_{\mathbb{n}}^{*}\rightarrow$
$\displaystyle\hat{a}^{\dagger}_{\mathbb{n}},$

which now fulfill the standard commutation rules
$[\hat{a}_{\mathbb{n}},\hat{a}_{{\mathbb{n}}^{\prime}}^{\dagger}]=\delta_{{\mathbb{n}}{\mathbb{n}}^{\prime}}$.
We now need to quantize also the position of the two walls. If we assume that
our system has a cylindrical symmetry along the $x$-axis and that in our frame
of reference the wall 1 is always at $x=0$, the second wall undergoes a
fluctuation characterized by two Fourier harmonics: $\Delta L_{x}=\Delta
L_{1}+\Delta L_{2}$. Such harmonic fluctuations do not interact with each
other and can be treated as two independent harmonic oscillators. Therefore,
the quantization of such degrees of freedom leads to:

$\displaystyle\Delta L_{1}\rightarrow$ $\displaystyle\delta
L_{1}(\hat{b}_{1}^{\dagger}+\hat{b}_{1}),$ (8) $\displaystyle\Delta
L_{2}\rightarrow$ $\displaystyle\delta
L_{2}(\hat{b}_{2}^{\dagger}+\hat{b}_{2}),$ (9)

where we introduced the annihilation and creation operators of two quantum
harmonic oscillators fulfilling the standard commutation relations:
$[\hat{b}_{1},\hat{b}_{1}^{\dagger}]=[\hat{b}_{2},\hat{b}_{2}^{\dagger}]=1$,
while all other commutators vanish. We notice that $\delta L_{1}$ and $\delta
L_{2}$ are the zero-point fluctuations of two harmonic oscillators having
different masses [37].

  * iv)

As last step, we rewrite the quantum Hamiltonian $\hat{H}$ in normal order and
we introduce two dimensionless amplitudes $\epsilon_{1}:=\delta L_{1}/L_{x}\ll
1$ and $\epsilon_{2}:=\delta L_{2}/L_{x}\ll 1$.

In the end, this procedure yields the Hamiltonian

$\displaystyle\hat{H}(t)=$ $\displaystyle\hat{H}_{0}+\hat{H}_{\textrm{I}},$
(10)

where each term reads

$\displaystyle\hat{H}_{0}:=$
$\displaystyle\sum_{\mathbb{n}}\omega_{\mathbb{n}}\,\hat{a}_{\mathbb{n}}^{\dagger}\hat{a}_{\mathbb{n}}+\omega_{1}\hat{b}_{1}^{\dagger}\hat{b}_{1}+\omega_{2}\hat{b}_{2}^{\dagger}\hat{b}_{2},$
$\displaystyle\hat{H}_{\textrm{I}}:=$ $\displaystyle
2\sum_{\mathbb{n}}\left[\frac{k(n_{y})^{2}+k(n_{z})^{2}}{\omega_{\mathbb{n}}}\hat{a}_{\mathbb{n}}^{\dagger}\hat{a}_{\mathbb{n}}-4\sum_{m_{x}}(-1)^{n_{x}+m_{x}}\frac{k(n_{x})k(m_{x})}{\sqrt{\omega_{\mathbb{n}}\,\omega_{m_{x},n_{y},n_{z}}}}\hat{X}_{\mathbb{n}}\hat{X}_{m_{x},n_{y},n_{z}}\right](\epsilon_{1}\hat{X}_{\textrm{b}1}+\epsilon_{2}\hat{X}_{\textrm{b}2}).$
(11)

In order to simplify the notation, we introduced the wave vector $k(n_{w})=\pi
n_{w}/L_{w}$, with $w=x,y,z$, the quadrature position operators
$\hat{X}_{\textrm{b},j}=\frac{1}{2}(\hat{b}_{j}^{\dagger}+\hat{b}_{j})$, with
$j=1,2$, and
$\hat{X}_{\mathbb{n}}=\frac{1}{2}(\hat{a}_{\mathbb{n}}^{\dagger}+\hat{a}_{\mathbb{n}})$.
We note that the ambiguity on the negative sign in $\hat{H}_{\textrm{I}}$ is
solved by including all terms of the Taylor expansion with respect to $\delta
L$ [28].

For our purposes, such Hamiltonian can be drastically simplified by assuming:

  1. 1.

The constraint $L_{x}\gg L_{y},L_{z}$ on the magnitude of the length of the
edges of the piston. This is motivated by the fact that there are no
excitations initially present in the $y$ and $z$ degrees of freedom. Given the
higher energy required to excite these degrees of freedom (since the energy
gaps are inversely proportional to the corresponding length) it is reasonable
to assume that they will remain unexcited. Thus, we can drop the first term in
the square brackets and obtain Hamiltonian (1) in the main text.

  2. 2.

The presence of only one cavity mode, say the fundamental mode
$\omega_{1,1,1}=\omega_{\textrm{c}}$. This is a reasonable assumption, since
other cavity modes with $n_{x}>1$ are initialized in the vacuum state.

Under such assumptions, the system Hamiltonian is reduced to Eq. (1) of the
main text.

##  Appendix B The master equation in the dressed picture and the dressed
operators

In this section we want to review the necessary tools to describe the time
evolution of the quantities of interest. Working in the Schrödinger picture,
we first need to solve the master equation for the density operator; however,
since we are dealing with a strongly interacting system, the best way to
proceed is to employ the master equation in the dressed picture [46]. To do
this, first let us introduce the transition amplitudes for the canonical
position operators calculated on the dressed basis: $c_{ij}=\langle
i\lvert\hat{a}+\hat{a}^{\dagger}\rvert j\rangle$, $u_{ij}=\langle
i\lvert\hat{b}_{1}+\hat{b}_{1}^{\dagger}\rvert j\rangle$ and $v_{ij}=\langle
i\lvert\hat{b}_{2}+\hat{b}_{2}^{\dagger}\rvert j\rangle$, where the state
$\rvert i\rangle$ is the $i$-th eigenstate of the Hamiltonian with eigenenergy
$E_{i}$.

We assume that the three subsystems are coupled to three different baths: in
particular, the wall 1 is coupled to a cold bath with damping rate
$\gamma_{1}$, the wall 2 is coupled to a hot bath with damping rate
$\gamma_{2}$. Finally, we also assume that the cavity always weakly interacts
with its own bath at $T\simeq 0$, with damping rate $\kappa\simeq 0$. Although
it does not play an active role in our dynamics, the interaction with the
third bath whose temperature is not exactly zero is expected in experimental
scenarios and prevents the violation of the third law of thermodynamics.

The master equation in the dressed picture has been obtained before [46, 47],
and it reads

$\frac{d\hat{\rho}}{dt}=-i[\hat{H},\hat{\rho}]+(\hat{\mathcal{L}}_{c}+\hat{\mathcal{L}}_{u}+\hat{\mathcal{L}}_{v})\hat{\rho},$
(12)

where we have defined

$\displaystyle\hat{\mathcal{L}}_{x}\hat{\rho}=y\sum_{j,i>j}\lvert
x_{ij}\rvert^{2}\left\\{n_{ij}(T)\mathcal{D}[\hat{P}_{ij}]\hat{\rho}+(1+n_{ij}(T))\mathcal{D}[\hat{P}_{ji}]\hat{\rho}\right\\}$
(13)

that needs to be supplemented by the quantities $x=c,u,v$, the rates of losses
$y=\gamma_{1},\gamma_{2},\kappa$, the thermal excitation numbers
$n_{ij}(T)=(e^{(E_{i}-E_{j})/T}-1)^{-1}$, the superoperators

$\displaystyle\mathcal{D}[\hat{P}_{ij}]\hat{\rho}=\frac{1}{2}\bigl{(}2\hat{P}_{ij}\hat{\rho}\hat{P}_{ij}^{\dagger}-\hat{\rho}\hat{P}_{ij}^{\dagger}\hat{P}_{ij}-\hat{P}_{ij}^{\dagger}\hat{P}_{ij}\hat{\rho}\bigr{)},$
(14)

and the transition operators $\hat{P}_{ij}=\lvert i\rangle\langle j\rvert$.

In order to evaluate the quantity of interest, it is necessary to define a set
of dressed annihilation operators for the various subsystems, and we have

$\displaystyle\hat{A}=$ $\displaystyle\sum_{j,i>j}c_{ij}\hat{P}_{ij},$
$\displaystyle\hat{B}_{1}=$ $\displaystyle\sum_{j,i>j}u_{ij}\hat{P}_{ij},$
$\displaystyle\hat{B}_{2}=$ $\displaystyle\sum_{j,i>j}v_{ij}\hat{P}_{ij}.$
(15)

We recall that the photon as well as the phonon population at any instant $t$
of time is given by $N_{c}(t)=\textrm{Tr}[\hat{A}^{\dagger}\hat{A}\rho(t)]$
and
$N_{\textrm{w}_{j}}(t)=\textrm{Tr}[\hat{B}_{j}^{\dagger}\hat{B}_{j}\rho(t)]$
($j=1,2$), respectively.

##  Appendix C The external drive

The total Hamiltonian includes a time-dependent term acting as an external
drive that periodically shifts the effective frequency of cavity mode from
$\tilde{\omega}_{\textrm{c},1}$ to $\tilde{\omega}_{\textrm{c},2}$ and
backwards. From a physical perspective, the role of such external drive is to
simulate the compression and the expansion of the cavity, thereby activating
the resonant phonon-photon conversion with either
$\tilde{\omega}_{\textrm{c},1}$ or $\tilde{\omega}_{\textrm{c},2}$. The
explicit form of the time-dependent term is:
$\hat{H}_{\textrm{dr}}(t)=f(t)\Delta\omega\hat{A}^{\dagger}\hat{A}$, where
$\Delta\omega=\tilde{\omega}_{\textrm{c},2}-\tilde{\omega}_{\textrm{c},1}$,
and $\hat{A},\hat{A}^{\dagger}$ are the cavity dressed operators in Eq. (15).
The function $f(t)$ is a periodic smooth step function which allows us to
rapidly vary the frequency of the cavity during the adiabatic transformations.
Its explicit form is

$\displaystyle f(t)=$
$\displaystyle\sum_{i}^{N}\left.\\{\sin^{2}[\Omega(t-t_{i})]\theta[t-t_{i}]\right.+\sin^{2}\left[\Omega\left(t-t_{i}-\tau\right)\right]\theta\left[t-t_{i}-\tau\right]$
$\displaystyle-\sin^{2}\left[\Omega\left(t-t_{i}-\Delta
t\right)\right]\theta\left[t-t_{i}-\Delta
t\right]\left.-\sin^{2}\left[\Omega\left(t-t_{i}-\tau-\Delta
t\right)\right]\theta\left[t-t_{i}-\tau-\Delta t\right]\right\\},$ (16)

where $t_{i}$ indicate the instants of time when the cycle is run, $\Delta t$
is the duration of the hot isochoric, $\tau$ is the duration of the two
adiabatics, and $\Omega=2\pi/\tau$. $\theta[t]$ is the Heaviside function. The
duration of the cold isochoric was estimated such that $\Delta\mathcal{U}$
reaches zero at the end of the transformation (see Fig. 3 of the main text),
and it corresponds to $t_{2}-t_{1}-2\tau-\Delta t$, whereas the duration of
one cycle is $t_{2}-t_{1}$.


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11institutetext: Fraunhofer Institute for Applied Information Technology,
Germany
11email<EMAIL_ADDRESS>
22institutetext: University Hospital of Cologne, Germany
33institutetext: University of Koblenz, Germany
33email<EMAIL_ADDRESS>
44institutetext: School of Future Science and Engineering, Soochow University,
China
44email<EMAIL_ADDRESS>
# Falcon 7b for Software Mention Detection in Scholarly Documents

AmeerAli Khan 11 Qusai Ramadan 33 0000-0001-8159-918X Cong Yang 44
0000-0002-8314-0935 Zeyd Boukhers 1122 0000-0001-9778-9164

###### Abstract

This paper aims to tackle the challenge posed by the increasing integration of
software tools in research across various disciplines by investigating the
application of Falcon-7b for the detection and classification of software
mentions within scholarly texts. Specifically, the study focuses on solving
Subtask I of the Software Mention Detection in Scholarly Publications (SOMD),
which entails identifying and categorizing software mentions from academic
literature. Through comprehensive experimentation, the paper explores
different training strategies, including a dual-classifier approach, adaptive
sampling, and weighted loss scaling, to enhance detection accuracy while
overcoming the complexities of class imbalance and the nuanced syntax of
scholarly writing. The findings highlight the benefits of selective labelling
and adaptive sampling in improving the model’s performance. However, they also
indicate that integrating multiple strategies does not necessarily result in
cumulative improvements. This research offers insights into the effective
application of large language models for specific tasks such as SOMD,
underlining the importance of tailored approaches to address the unique
challenges presented by academic text analysis.

###### Keywords:

Falcon Entity Recognition Mention Detection Scholarly Data Analysis.

##  1 Introduction

The integration of software tools into scientific research is no longer
confined to engineering disciplines but has extended to all disciplines,
including the humanities and social sciences. This is largely driven by the
escalating need to process and analyze data across various domains.
Consequently, an extensive mention of these tools in the scientific articles.
Furthermore, the volume of published scholarly articles continues to grow year
after year, which makes overcoming the challenge of managing this vast
repository of knowledge more important than ever before. In response, numerous
projects and initiatives such as EOSC111https://eosc-portal.eu/ and
NFDI222https://www.nfdi.de/ have been launched to organize research outputs,
including articles, software mentions, and datasets, in a manner that adheres
to the FAIR principles [27] (i.e.Findable, Accessible, Interoperable, and
Reusable) to enhance the overall integrity and reproducibility of scientific
research.

The absence of a standardized mechanism for authors to accurately cite and
reference tools and datasets in their scholarly articles necessitates the
extraction of such mentions post-publication. However, this task is
challenging due to the unstructured nature of these articles. This underscores
the importance of developing sophisticated and reliable methodologies capable
of automatically and accurately recognizing mentions of these tools. This
paper addresses this challenge by concentrating on a key aspect of it:
"_Subtask I of the Software Mention Detection in Scholarly Publications
(SOMD)_." 333https://nfdi4ds.github.io/nslp2024/docs/somd_shared_task.html The
aim is to explore new methodologies and models of software mention detection
processes in academic literature.

Although the challenge of detecting software mentions has been directly
addressed using the KG approach [22, 20], a lot of approaches that solve the
general problem have been proposed to solve the general problem of extracting
information from scholarly data, including Named Entity Recognition [23],
Metadata Extraction [5, 10, 1] and Reference Extraction and Segmentation [4,
19, 8]. The proven capabilities of large language models (LLMs) to understand
and generate human-like text offer new possibilities. Among the advanced
models, the LLM such as the Falcon-7b model stands out due to its decoder-only
architecture and the breadth of its training data. Although it was initially
designed for generative tasks, the scale of architecture and the breadth of
its training data present an exciting opportunity for exploring its potential
for application in specialized areas of NLP, such as the detection and
classification of software mentioned in academic publications.

This paper investigates the effectiveness of the Falcon-7b model on the task
of software mention detection in the scientific literature by adapting it to
the task. The choice of model is arbitrary without assuming it has a specific
advantage over similar models like LLAMA 2 [24] or GPT3.5 [6]. This choice
allows us to explore how well such LLM models perform on a specialized task,
specifically, we leverage the model’s extensive training on a wide array of
texts and its advanced understanding of linguistic nuances. This effectiveness
is critically assessed through comprehensive experiments, encompassing a
variety of evaluation metrics to ensure a balanced analysis of the model’s
applicability to the task at hand.

The structure of this paper is laid out as follows: Section 2 provides a
review of the relevant literature. In Section 3, we delve into the methodology
of this study, outlining the approaches and techniques utilized. Section 4
presents the experimental setup, alongside the results achieved from our
investigations. Finally, Section 5 concludes the paper, summarizing our
findings and offering insights into potential avenues for future research.

##  2 Related Work

As there are not so many efforts to detect software mention using LLM, we
review in this section approaches on named-entity recognition (NER), where we
consider that software mention detection is a use case of this problem. This
review is structured in three categories:

###  2.1 Rule-based and Classical Machine Learning Approaches

Named entity recognition has been at the core of machine learning research for
decades due to its importance in a variety of applications. However, the task
is challenging and thus many approaches have been proposed to tackle the
problem in specific scenarios. [2] introduces a rule-based NER framework
designed for the Malay language, to improve the retrieval process of articles.
It addresses the challenges faced by NER processes in languages with
morphological differences and the lack of existing systems for the Malay
language. By analyzing the domain of studies and the specific linguistic
features of Malay, this framework accurately classifies named entities such as
people, organizations, and locations. [16] proposes to address the limitations
of traditional rule-based approaches by using Hidden Markov Models (HMM) for
NER tasks in Indian Language beyond domain-specific applications. [25]
proposes an approach using the Conditional Random Field (CRF) and Active
Learning (AL) algorithm, where the training process of the CRF classifier is
repeated until the model stabilizes. This resulted in an efficient and cost-
effective outcome. [9] uses the Beam search algorithm to detect named entities
in the Persian language by segmenting text into suitable and unsuitable
expressions for the named entities and then applying dynamic external
knowledge to recognize the emerging named entity.

###  2.2 Deep Learning-based Approaches

Deep Neural Networks have proven significant performance over classical
machine learning approaches on different tasks, including NLP, computer vision
and others. Consequently, they have been used to address NER tasks as well
[12, 14]. [29] proposes a NER framework called E-NER that uses evidential deep
learning (EDL) to explicitly model predictive uncertainty for named entity
recognition (NER) tasks. It addresses the challenges of sparse entities and
out-of-vocabulary (OOV) entities in NER by introducing uncertainty-guided loss
terms and training strategies. E-NER achieves accurate uncertainty estimation,
better OOV/OOD detection performance, and improved generalization ability on
OOV entities compared to state-of-the-art baselines. [15] introduces a novel
approach to Clinical NER for de-identifying sensitive health information in
clinical texts by developing a Capsule-LSTM network that leverages the
strengths of capsule networks for capturing complex data relationships and
LSTM networks for understanding sequential data. [13] the All CNN (ACNN) model
for Chinese clinical NER that employs CNN enhanced by an attention mechanism,
sidestepping the inefficiencies of traditional LSTM models. By leveraging
multi-level CNN layers with various kernel sizes and a residual structure,
ACNN adeptly captures context information across different scales, addressing
the challenges posed by the complex grammar and terminology of Chinese
clinical texts. [7] proposes to combine CNN and bi-LSTM architectures for
biomedical NER (bioNER), aiming to efficiently handle the complexities of
biomedical texts, such as variant spellings and inconsistent use of prefixes
and suffixes. The proposed combinatorial feature embedding and attention
mechanism for enhanced entity recognition demonstrate superior performance on
benchmark datasets JNLPBA and NCBI-Disease when compared with existing
methods.

###  2.3 Large Language Model-based Approaches

Due to their power to understand and generate natural text, LLMs have been
employed for many Natural Language Processing (NLP) tasks, including Named
Entity recognition. [26] proposes GPT-NER, a method that transforms the
sequence labelling task of Named Entity Recognition (NER) into a text
generation task, allowing large language models (LLMs) to be easily adapted
for NER. GPT-NER achieves comparable performances to fully supervised
baselines on five widely adopted NER datasets and exhibits a greater ability
in low-resource and few-shot setups, making it suitable for real-world NER
applications with limited labelled examples. [17] employs Generative Pre-
trained Transformer 3 (GPT-3) by OpenAI together with a weak supervisor to
address the NER challenge within the legal domain, exemplified by documents
from the Official Gazette of the Federal District (DODF). [11] proposes an
architecture that refines the adversarial example generation process for LLM
using disentanglement and word attribution techniques to efficiently generate
adversarial examples while maintaining semantic similarity. The experiments
conducted on benchmark datasets—CoNLL-2003, Ontonotes 5.0, and
MultiCoNER—demonstrated that the approach improves the F1 scores by 8%.

##  3 Method

This section elaborates on the methodologies applied for the Software Mention
Detection in Scholarly Publications (SOMD) [21] Subtask I, part of the Natural
Scientific Language Processing and Research Knowledge Graphs (NSLP)
444https://nfdi4ds.github.io/nslp2024/ 2024 workshop. Our approach is centred
on token classification, addressing the unique challenges software mention
recognition poses in scientific texts.

The primary objective of the subtask is to recognize software mentions within
individual sentences, further classifying them by mention type (e.g., mention,
usage, creation) and software type (e.g., application, programming
environment, package). The task is approached with a methodology that
innovatively applies a large language model (LLM), such as the Falcon-7b [3]
model, as the foundation for a token classification system.

The core of our methodology is The Falcon-7b model, which is a decoder-only
architecture known for its performance across a wide range of NLP tasks.
Despite its primary design as a generative model, we adapt Falcon-7b for token
classification by appending a classification layer atop its structure. This
adaptation is driven by the hypothesis that the extensive pre-training on
diverse corpora, coupled with its vast parameter space, provides the Falcon-7b
model with a nuanced understanding of textual context. Such capabilities can
significantly enhance the model’s proficiency in identifying and classifying
software mentions within the complex syntax and semantics of scholarly
writing.

The methodology implemented in this study is structured around several
strategic training approaches, tailored to address the intrinsic challenges of
the SOMD task. Initially, the task is framed as a token classification
problem, where labels are assigned to each word or subtoken within a sentence
to denote the presence and category of software mentions. A notable challenge
arises from the tendency of transformer-based models like Falcon-7b to segment
words into multiple subtokens, which complicates the direct application of
labels.

To address the challenge of labelling consistency in the presence of subtoken
segmentation by transformer models, our methodology employs two distinct
strategies. The first, referred to as "Unified Labeling" assigns the same
label to all subtokens derived from a single word’s segmentation, ensuring
consistency across the subtoken sequence. This maintains label continuity
across divisions, which facilitates coherent entity recognition despite the
segmentation process. In contrast, the second strategy "Selective Labeling"
assigns a label only to the first subtoken of a segmented word, disregarding
subsequent subtokens. This method aims to minimize label redundancy and
computational complexity associated with processing multiple labels for a
single entity. Each approach is independently explored to determine its
efficacy in addressing the challenges of subtoken label alignment in the
context of the SOMD task.

A critical obstacle encountered in the SOMD task is the substantial class
imbalance, where data is skewed towards non-mention (’O’) labels. To address
this imbalance, we implemented two distinct and independently tested
strategies to recalibrate the dataset for training. In the first strategy
"Weighted Loss", weighted loss is applied, where class weights are inversely
proportional to class frequencies. however, given the substantial imbalance,
original weight values became impractical for underrepresented classes. To
resolve this, we scaled the weights within a sensible range, setting minimums
and maximums (1, and thresholds of 25, 50, 100, and 200), thereby enabling the
nuanced training of models across various weight configurations to explore
their efficacy in balancing classification performance. The second strategy
"Adaptive Sampling" strategically segments the dataset into over-represented
(all ’O’ tokens) and under-represented (at least one non-’O’ tokens)
categories. This involves oversampling the under-represented data by a factor
of 2 and undersampling the over-represented data to sizes equal to multiples
(1, 1.5, 3) of the oversampled data volume. Adaptive Sampling aims to achieve
a more balanced class distribution, enhancing the model’s capacity to learn
from a representative spectrum of the dataset. Each strategy’s independent
evaluation provides insights into its effectiveness in addressing dataset
imbalance challenges in the SOMD task.

Additionally, recognizing the multifaceted nature of software mentions,
separate token classifiers are developed for identifying software types and
the mentioned types. We call this strategy "Dual-Classifier". It enables more
precise label application by separating the task into two distinct
classification problems, by distinguishing between software and mention types.
This setup is designed to explore whether such a nuanced approach can
effectively capture the diverse nature of software mentions, offering a
potentially more sophisticated mechanism for their identification and
classification.

To ensure the effectiveness and generalizability of the model, the pre-defined
training dataset was utilized to develop and refine the model’s capabilities.
For evaluating the model’s performance in accurately identifying and
classifying software mentions, the test dataset provided for Subtask II was
employed. With this, we aim to conduct a comprehensive assessment of the
model’s ability to generalize across various scenarios and text variations
found in scholarly publications, thereby validating the model’s applicability
and effectiveness in real-world tasks.

Following the comprehensive methodologies delineated for the Software Mention
Detection (SOMD) task, our evaluation process is designed to rigorously assess
the effectiveness of our approaches, namely the "Unified Labeling," "Selective
Labeling," "Weighted Loss," "Adaptive Sampling," and the "Dual-Classifier"
Approach. Central to our evaluation is the F1-Score, focusing on exact
matches, which serves as a critical metric to quantify the precision and
recall of our models in accurately identifying and classifying software
mentions. Adherence to the IOB2 format for our submission files ensures our
alignment with the standardized training labels, facilitating direct
comparison of our model’s performance against established benchmarks.

##  4 Experimental Results

###  4.1 Results

To evaluate our method on Software Mention Detection in Scholarly Publications
(SOMD) Subtask I, we explored various settings centred around the Falcon-7b
model. The experiments are conducted using the Hugging Face Transformers
library[28], with PyTorch [18] as the computational backend. Model training
and evaluation were performed on a high-performance computing cluster equipped
with NVIDIA A100 GPUs. To maintain consistency across all experiments
conducted in this study, we standardized our training hyperparameters. This
ensures that any observed differences in model performance are attributable to
the variations in model architecture, data preprocessing, or other
experimental conditions, rather than inconsistencies in training
configurations. The hyperparameters used throughout our experiments are
summarized in Table LABEL:table:hyperparameters (Appendix LABEL:sec:app).

The focal point of our evaluation is the F1 score, which balances precision
and recall and offers a comprehensive measure of model performance. The
evaluation result on the test dataset is illustrated in Table 1. These results
are submitted to the shared task platform under the username: “fddaFIT”.

Table 1: Evaluation metrics for each experimental approach. Method | Precision | Recall | F1 Score
---|---|---|---
Unified Labeling | 0.6769 | 0.4718 | 0.5561
Selective Labeling | 0.7563 | 0.5243 | 0.6193
Adaptive Sampling multiples@1 | 0.6496 | 0.4932 | 0.5607
Adaptive Sampling<EMAIL_ADDRESS>| 0.7480 | 0.5417 | 0.6284
Adaptive Sampling multiples@3 | 0.7213 | 0.4874 | 0.5817
Weighted loss scaled@25 | 0.7559 | 0.4990 | 0.6012
Weighted loss scaled@50 | 0.7211 | 0.4971 | 0.5885
Weighted loss scaled@100 | 0.7195 | 0.4932 | 0.5853
Weighted loss scaled@200 | 0.7110 | 0.4874 | 0.5783
Dual-Classifier | 0.7602 | 0.5048 | 0.6068
Dual-Classifier + Adaptive Sampling<EMAIL_ADDRESS>| 0.7602 | 0.5048 | 0.6068

In comparison between the two distinct labelling strategies: "Unified
Labeling" and "Selective Labeling." The outcome favoured the "Selective
Labeling" strategy, which demonstrated superior precision and recall and
achieved a higher F1 score of $0.6193$ compared to the $0.5561$ of "Unified
Labeling." This demonstrates the effectiveness of selectively assigning labels
in enhancing the model’s precision and recall. This finding guided the
direction of subsequent experiments, by embedding the "Selective Labeling"
strategy in our methodology.

Further investigations focus on adaptive sampling and weighted loss scaling to
address the notable challenge of dataset imbalance. Adaptive sampling
experiments, applying various undersampling multipliers to over-represented
data, demonstrated the precise impact of data distribution on model efficacy.
The employment of a multiplier of 1.5 showed an enhancement of the F1 score to
$0.6284$, the highest among adaptive sampling variations. This suggests an
optimal balance in dataset composition, significantly contributing to model
performance.

Experiments with weighted loss, adjusted across a range of maximum weights
(25, 50, 100, and 200), aimed to refine the model’s sensitivity to class
frequencies. While experimenting with weighted loss scaling offered insights
into handling class imbalance, the adjustments did not surpass the adaptive
sampling’s peak F1 score, with the highest recorded F1 at $0.6012$ for a
scaling factor of $25$.

The "Dual-Classifier" approach introduced a bifurcated strategy for
identifying software types and mention types, aiming to enrich the model’s
understanding and classification accuracy. Interestingly, this approach alone
achieved an F1 score of 0.6068, comparable to some weighted loss scaling
strategies but slightly below the best-performing adaptive sampling method.
Combining the "Dual-Classifier" with "Adaptive Sampling" at a multiplier of
1.5 did not further enhance the F1 score, indicating that while each method
independently contributes to addressing specific challenges in SOMD, their
combined effect does not necessarily result in cumulative improvements.

The experiments demonstrate the critical role of selective labelling and
adaptive sampling in enhancing F1 scores for SOMD. While weighted loss scaling
and the "Dual-Classifier" approach contribute to performance improvements, the
combination of strategies does not yield further enhancements. This indicates
the necessity of strategic selection and implementation in model development
for SOMD tasks.

In these experiments, we observed that the model effectively identifies
software mentions within the complex academic text and accurately classifies
entities like specific software tools or programming languages.

For example, as shown in Table LABEL:table:confusion_usage_mention (Appendix
LABEL:sec:app), it might correctly identify "Python" as a programming language
used within a research context. However, challenges arise in distinguishing
between mentions of software and instances where the software is being
actively used or discussed in depth. This differentiation is crucial for
understanding the role of software in research, as only mentions might not
signify importance or relevance to the study’s outcomes. Examples of the
model’s output are provided in the full
version555https://zenodo.org/doi/10.5281/zenodo.10993039 of this paper.

##  5 Conclusion

In this paper, we presented the efficacy of the Falcon-7b model, a prominent
Large Language Model (LLM), in tackling the nuances of Software Mention
Detection (SOMD) within scholarly publications. Guided by the hypothesis that
advanced LLMs could significantly improve the precision and recall for SOMD
tasks due to their extensive training on diverse datasets, our study
systematically explored various strategies centred around the Falcon-7b model.

The comparative analysis of "Unified Labeling" and "Selective Labeling"
strategies revealed a preference for "Selective Labeling," which yielded a
higher F1 score. This result underscores the incremental nature of
advancements achievable with the Falcon-7b model in the context of SOMD tasks.
Additionally, our experiments with adaptive sampling and weighted loss scaling
aimed at addressing dataset imbalances highlighted that, despite certain
improvements, the enhancements were not as substantial as anticipated. The
adaptive sampling strategy, especially with a multiplier of 1.5, did indeed
enhance the F1 score, to the highest obtained score. However, this observation
was not sufficient to categorize the performance as extraordinary. This
finding suggests that while the Falcon-7b model and similar LLMs hold promise
for NLP tasks, their application in specialized areas such as SOMD may not
always yield groundbreaking results.

In conclusion, the outcomes of our study indicate that, despite the advanced
capabilities of LLMs like Falcon-7b, the performance improvements in specific
NLP tasks such as SOMD are modest. While LLMs offer advantages in processing
and understanding complex language patterns, their effectiveness in
specialized domains like software mention detection within scholarly texts
does not markedly outperform more traditional approaches. This emphasizes the
importance of combining LLMs with other approaches and the need to explore a
broad spectrum of models and methodologies to identify the most effective
solutions for specialized NLP challenges.

## Acknowledgement

This work was funded by the FAIR Data Spaces project of the German Federal
Ministry of Education and Research (BMBF) under grant numbers FAIRDS05 and
FAIRDS15 and by NFDI4DS project with grant number 460234259.

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