* Anderson et al. [2013] Anderson, J. A., Jankowski, E., Grubb, T. L., Engel, M., and Glotzer, S. C. (2013).  Massively parallel Monte Carlo for many-particle simulations on GPUs.  _Journal of Computational Physics_ 254, 27–38.  http://dx.doi.org/10.1016/j.jcp.2013.07.023
  * Baik and Liu [2016] Baik, J. and Liu, Z. (2016).  TASEP on a Ring in Sub-relaxation Time Scale.  _Journal of Statistical Physics_ 165, 1051–1085.  10.1007/s10955-016-1665-y
  * Baxter [1982] Baxter, R. J. (1982).  _Exactly solved models in statistical mechanics_ (London: Academic Press)
  * Berg [2004] Berg, B. A. (2004).  _Markov Chain Monte Carlo simulations and their statistical analysis: with web-based Fortran code_ (World Scientific)
  * Bernard [2011] Bernard, E. (2011).  _Algorithms and applications of the Monte Carlo method: Two-dimensional melting and perfect sampling_.  Ph.D. thesis, Université Pierre et Marie Curie - Paris VI
  * Bernard and Krauth [2011] Bernard, E. P. and Krauth, W. (2011).  Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition.  _Phys. Rev. Lett._ 107, 155704.  10.1103/PhysRevLett.107.155704
  * Bernard et al. [2009] Bernard, E. P., Krauth, W., and Wilson, D. B. (2009).  Event-chain Monte Carlo algorithms for hard-sphere systems.  _Phys. Rev. E_ 80, 056704.  10.1103/PhysRevE.80.056704
  * Berthoumieux and Maggs [2010] Berthoumieux, H. and Maggs, A. C. (2010).  Collective dispersion forces in the fluid state.  _EPL_ 91, 56006
  * Bierkens et al. [2018] Bierkens, J., Bouchard-Côté, A., Doucet, A., Duncan, A. B., Fearnhead, P., Lienart, T., et al. (2018).  Piecewise Deterministic Markov Processes for Scalable Monte Carlo on Restricted Domains.  _Statistics and Probability Letters_ 136, 148–154
  * Bierkens and Roberts [2017] Bierkens, J. and Roberts, G. (2017).  A piecewise deterministic scaling limit of lifted Metropolis–Hastings in the Curie–Weiss model.  _The Annals of Applied Probability_ 27, 846–882.  10.1214/16-aap1217
  * Bouchard-Côté et al. [2018] Bouchard-Côté, A., Vollmer, S. J., and Doucet, A. (2018).  The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method.  _Journal of the American Statistical Association_ 113, 855–867.  10.1080/01621459.2017.1294075
  * Chen et al. [1999] Chen, F., Lovász, L., and Pak, I. (1999).  Lifting Markov Chains to Speed up Mixing.  _Proceedings of the 17th Annual ACM Symposium on Theory of Computing_ , 275
  * Chou et al. [2011] Chou, T., Mallick, K., and Zia, R. K. P. (2011).  Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport.  _Reports on Progress in Physics_ 74, 116601
  * de Leeuw et al. [1980] de Leeuw, S. W., Perram, J. W., and Smith, E. R. (1980).  Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants.  _Proc. R. Soc. A_ 373, 27–56.  10.1098/rspa.1980.0135
  * Devroye [1986] Devroye, L. (1986).  _Non-Uniform Random Variate Generation_ (Springer New York).  10.1007/978-1-4613-8643-8
  * Dhar [1987] Dhar, D. (1987).  An exactly solved model for interfacial growth.  _Phase Transitions_ 9, 51.  10.1080/01411598708241334
  * Diaconis et al. [2000] Diaconis, P., Holmes, S., and Neal, R. M. (2000).  Analysis of a nonreversible Markov chain sampler.  _Ann. Appl. Probab._ 10, 726–752
  * Diaconis et al. [2011] Diaconis, P., Lebeau, G., and Michel, L. (2011).  Geometric analysis for the Metropolis algorithm on Lipschitz domains.  _Inventiones mathematicae_ 185, 239–281.  10.1007/s00222-010-0303-6
  * Dress and Krauth [1995] Dress, C. and Krauth, W. (1995).  Cluster algorithm for hard spheres and related systems.  _Journal of Physics A Mathematical General_ 28, L597–L601.  10.1088/0305-4470/28/23/001
  * Engel et al. [2013] Engel, M., Anderson, J. A., Glotzer, S. C., Isobe, M., Bernard, E. P., and Krauth, W. (2013).  Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods.  _Phys. Rev. E_ 87, 042134.  10.1103/PhysRevE.87.042134
  * Faulkner et al. [2018] Faulkner, M. F., Qin, L., Maggs, A. C., and Krauth, W. (2018).  All-atom computations with irreversible Markov chains.  _J. Chem. Phys._ 149, 064113.  10.1063/1.5036638
  * Fernandes and Weigel [2011] Fernandes, H. C. and Weigel, M. (2011).  Non-reversible Monte Carlo simulations of spin models.  _Computer Physics Communications_ 182, 1856–1859.  10.1016/j.cpc.2010.11.017
  * Fill [1991] Fill, J. A. (1991).  Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process.  _The Annals of Applied Probability_ 1, 62–87.  10.1214/aoap/1177005981
  * Frenkel and Smit [2001] Frenkel, D. and Smit, B. (2001).  _Understanding Molecular Simulation: From Algorithms to Applications_.  Computational science series (Elsevier Science)
  * Fröhlich and Spencer [1981] Fröhlich, J. and Spencer, T. (1981).  The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas.  _Communications in Mathematical Physics_ 81, 527–602.  10.1007/BF01208273
  * Gamma et al. [1994] Gamma, E., Helm, R., Johnson, R., and Vlissides, J. M. (1994).  _Design Patterns: Elements of Reusable Object-Oriented Software_ (Addison-Wesley Professional), 1 edn.
  * Greenberg et al. [1996] Greenberg, A. G., Lubachevsky, B. D., and Mitrani, I. (1996).  Superfast parallel discrete event simulations.  _ACM Transactions on Modeling and Computer Simulation (TOMACS)_ 6, 107–136
  * Gwa and Spohn [1992] Gwa, L.-H. and Spohn, H. (1992).  Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian.  _Phys. Rev. Lett._ 68, 725–728.  10.1103/PhysRevLett.68.725
  * Harland et al. [2017] Harland, J., Michel, M., Kampmann, T. A., and Kierfeld, J. (2017).  Event-chain Monte Carlo algorithms for three- and many-particle interactions.  _EPL (Europhysics Letters)_ 117, 30001
  * Hasenbusch [2005] Hasenbusch, M. (2005).  The two-dimensional XY model at the transition temperature: a high-precision Monte Carlo study.  _Journal of Physics A: Mathematical and General_ 38, 5869
  * Hasenbusch [2019] Hasenbusch, M. (2019).  Monte Carlo study of an improved clock model in three dimensions.  _Phys. Rev. B_ 100, 224517.  10.1103/PhysRevB.100.224517
  * Hayes and Janes [2013] Hayes, T. and Janes, M. (2013).  Local Liftings with Optimal Speedup for Arbitrary Distributions over a Path.  Unpublished manuscript
  * Hildebrand [2004] Hildebrand, M. (2004).  Rates of convergence of the Diaconis-Holmes-Neal Markov chain sampler with a V-shaped stationary probability.  _Markov Proc. Rel. Fields_ 10, 687–704
  * Höllmer et al. [2020] Höllmer, P., Qin, L., Faulkner, M. F., Maggs, A., and Krauth, W. (2020).  JeLLyFysh-Version1.0 — a Python application for all-atom event-chain Monte Carlo.  _Comput. Phys. Commun._ 253, 107168.  10.1016/j.cpc.2020.107168
  * Hu and Charbonneau [2018] Hu, Y. and Charbonneau, P. (2018).  Clustering and assembly dynamics of a one-dimensional microphase former.  _Soft Matter_ 14, 4101–4109.  10.1039/c8sm00315g
  * Isobe [2016] Isobe, M. (2016).  Hard sphere simulation in statistical physics methodologies and applications.  _Molecular Simulation_ 42, 1317–1329.  10.1080/08927022.2016.1139106
  * Isobe and Krauth [2015] Isobe, M. and Krauth, W. (2015).  Hard-sphere melting and crystallization with event-chain Monte Carlo.  _The Journal of Chemical Physics_ 143, 084509.  10.1063/1.4929529
  * Jaster [1999] Jaster, A. (1999).  An improved Metropolis algorithm for hard core systems.  _Physica A: Statistical Mechanics and its Applications_ 264, 134 – 141.  https://doi.org/10.1016/S0378-4371(98)00337-9
  * Kampmann et al. [2015] Kampmann, T. A., Boltz, H.-H., and Kierfeld, J. (2015).  Monte Carlo simulation of dense polymer melts using event chain algorithms.  _The Journal of Chemical Physics_ 143, 044105.  10.1063/1.4927084
  * Kannan et al. [2003] Kannan, R., Mahoney, M. W., and Montenegro, R. (2003).  Rapid mixing of several Markov chains for a hard-core model.  In _Proc. 14th annual ISAAC_ (Springer, Berlin, Heidelberg), Lecture Notes in Computer Science, 663–675.  10.1007/978-3-540-24587-2_68
  * Kapfer and Krauth [2013] Kapfer, S. C. and Krauth, W. (2013).  Sampling from a polytope and hard-disk Monte Carlo.  _Journal of Physics: Conference Series_ 454, 012031.  10.1088/1742-6596/454/1/012031
  * Kapfer and Krauth [2016] Kapfer, S. C. and Krauth, W. (2016).  Cell-veto Monte Carlo algorithm for long-range systems.  _Phys. Rev. E_ 94, 031302.  10.1103/PhysRevE.94.031302
  * Kapfer and Krauth [2017] Kapfer, S. C. and Krauth, W. (2017).  Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium.  _Phys. Rev. Lett._ 119, 240603.  10.1103/PhysRevLett.119.240603
  * Kimura and Higuchi [2017] Kimura, K. and Higuchi, S. (2017).  Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models.  _EPL_ 120, 30003.  10.1209/0295-5075/120/30003
  * Kirkpatrick et al. [1983] Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983).  Optimization by Simulated Annealing.  _Science_ 220, 671–680
  * Kosterlitz and Thouless [1973] Kosterlitz, J. M. and Thouless, D. J. (1973).  Ordering, metastability and phase transitions in two-dimensional systems.  _Journal of Physics C Solid State Physics_ 6, 1181–1203.  10.1088/0022-3719/6/7/010
  * Krantz [1996] Krantz, A. T. (1996).  Analysis of an Efficient Algorithm for the Hard-Sphere Problem.  _ACM Trans. Model. Comput. Simul._ 6, 185–209.  10.1145/235025.235030
  * Krauth [2006] Krauth, W. (2006).  _Statistical Mechanics: Algorithms and Computations_ (Oxford University Press)
  * Lacoin [2016] Lacoin, H. (2016).  The cutoff profile for the simple exclusion process on the circle.  _The Annals of Probability_ 44, 3399–3430.  10.1214/15-aop1053
  * Lei [2018] Lei, Z. (2018).  _Irreversible Markov Chains for Particle Systems and Spin Models: Mixing and Dynamical Scaling_.  Ph.D. thesis, École Normale Supérieure, Paris
  * Lei and Krauth [2018a] Lei, Z. and Krauth, W. (2018a).  Irreversible Markov chains in spin models: Topological excitations.  _EPL_ 121, 10008
  * Lei and Krauth [2018b] Lei, Z. and Krauth, W. (2018b).  Mixing and perfect sampling in one-dimensional particle systems.  _EPL_ 124, 20003
  * Lei et al. [2019] Lei, Z., Krauth, W., and Maggs, A. C. (2019).  Event-chain Monte Carlo with factor fields.  _Physical Review E_ 99\.  10.1103/physreve.99.043301
  * Levin et al. [2010] Levin, D. A., Luczak, M. J., and Peres, Y. (2010).  Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability.  _Probability Theory and Related Fields_ 146, 223–265.  10.1007/s00440-008-0189-z
  * Levin et al. [2008] Levin, D. A., Peres, Y., and Wilmer, E. L. (2008).  _Markov Chains and Mixing Times_ (American Mathematical Society)
  * Lewis and Shedler [1979] Lewis, P. A. W. and Shedler, G. S. (1979).  Simulation of nonhomogeneous Poisson processes by thinning.  _Naval Research Logistics Quarterly_ 26, 403–413.  10.1002/nav.3800260304
  * Li et al. [2020] Li, B., Todo, S., Maggs, A., and Krauth, W. (2020).  _Computer Physics Communications_ , 10770210.1016/j.cpc.2020.107702
  * Liu and Luijten [2004] Liu, J. and Luijten, E. (2004).  Rejection-Free Geometric Cluster Algorithm for Complex Fluids.  _Physical Review Letters_ 92\.  10.1103/physrevlett.92.035504
  * Lovász and Winkler [1998] Lovász, L. and Winkler, P. (1998).  _Mixing times_ (Providence RI: Amer. Math. Soc.), vol. 41.  85 – 134
  * Lubachevsky [1993] Lubachevsky, B. (1993).  Several unsolved problems in large-scale discrete event simulations.  _ACM SIGSIM Simulation Digest_ 23, 60–67.  10.1145/174134.158467
  * Lubachevsky [1992] Lubachevsky, B. D. (1992).  Simulating billiards serially and in parallel.  _International Journal in Computer Simulation_ 2, 373–411
  * Mak [2005] Mak, C. H. (2005).  Stochastic potential switching algorithm for Monte Carlo simulations of complex systems.  _The Journal of Chemical Physics_ 122, 214110.  10.1063/1.1925273
  * Marin [1997] Marin, M. (1997).  Billiards and related systems on the bulk-synchronous parallel model.  In _Proceedings 11th Workshop on Parallel and Distributed Simulation_. 164–171.  10.1109/PADS.1997.594602
  * Martinelli [1999] Martinelli, F. (1999).  Lectures on Glauber Dynamics for Discrete Spin Models.  In _Lectures on Probability Theory and Statistics: Ecole d’Eté de Probabilités de Saint-Flour XXVII - 1997_ , ed. P. Bernard (Berlin, Heidelberg: Springer Berlin Heidelberg). 93–191.  10.1007/978-3-540-48115-7_2
  * Mermin [1968] Mermin, N. D. (1968).  Crystalline Order in Two Dimensions.  _Physical Review_ 176, 250–254.  10.1103/PhysRev.176.250
  * Metropolis et al. [1953] Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953).  Equation of State Calculations by Fast Computing Machines.  _J. Chem. Phys._ 21, 1087–1092.  10.1063/1.1699114
  * Metropolis et al. [1953] Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953).  Equation of State Calculations by Fast Computing Machines.  _J. Chem. Phys._ 21, 1087–1092.  10.1063/1.1699114
  * Michel [2016] Michel, M. (2016).  _Irreversible Markov chains by the factorized Metropolis filter: Algorithms and applications in particle systems and spin models_.  Ph.D. thesis, Ecole Normale Superieure de Paris - ENS Paris
  * Michel et al. [2014] Michel, M., Kapfer, S. C., and Krauth, W. (2014).  Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps.  _J. Chem. Phys._ 140, 054116.  10.1063/1.4863991
  * Michel et al. [2015] Michel, M., Mayer, J., and Krauth, W. (2015).  Event-chain Monte Carlo for classical continuous spin models.  _EPL (Europhysics Letters)_ 112, 20003.  10.1209/0295-5075/112/20003
  * Miller and Luding [2004] Miller, S. and Luding, S. (2004).  Event-driven molecular dynamics in parallel.  _Journal of Computational Physics_ 193, 306 – 316.  10.1016/j.jcp.2003.08.009
  * Müller et al. [2020] Müller, D., Kampmann, T. A., and Kierfeld, J. (2020).  Chaining of hard disks in nematic needles: particle-based simulation of colloidal interactions in liquid crystals.  _Scientific Reports_ 10\.  10.1038/s41598-020-69544-4
  * Nielsen and Weber [2015] Nielsen, A. J. N. and Weber, M. (2015).  Computing the nearest reversible Markov chain.  _Numerical Linear Algebra with Applications_ 22, 483–499.  10.1002/nla.1967
  * Nishikawa et al. [2015] Nishikawa, Y., Michel, M., Krauth, W., and Hukushima, K. (2015).  Event-chain algorithm for the Heisenberg model: Evidence for z sim 1 dynamic scaling.  _Phys. Rev. E_ 92, 063306.  10.1103/PhysRevE.92.063306
  * O’Keeffe and Orkoulas [2009] O’Keeffe, C. J. and Orkoulas, G. (2009).  Parallel canonical Monte Carlo simulations through sequential updating of particles.  _J. Chem. Phys._ 130, 134109.  10.1063/1.3097528
  * Peters and de With [2012] Peters, E. A. J. F. and de With, G. (2012).  Rejection-free Monte Carlo sampling for general potentials.  _Phys. Rev. E_ 85, 026703.  10.1103/PhysRevE.85.026703
  * Plimpton [1995] Plimpton, S. (1995).  Fast Parallel Algorithms for Short-Range Molecular Dynamics.  _Journal of Computational Physics_ 117, 1–19.  10.1006/jcph.1995.1039
  * Qin et al. [2020] [Dataset] Qin, L., Hoellmer, P., and Krauth, W. (2020).  Fast sequential Markov chains
  * Randall and Winkler [2005a] Randall, D. and Winkler, P. (2005a).  Mixing Points on a Circle.  In _Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques: 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005, Berkeley, CA, USA, August 22-24, 2005. Proceedings_ , eds. C. Chekuri, K. Jansen, J. D. P. Rolim, and L. Trevisan (Berlin, Heidelberg: Springer Berlin Heidelberg). 426–435.  10.1007/11538462_36
  * Randall and Winkler [2005b] Randall, D. and Winkler, P. (2005b).  Mixing Points on an Interval.  In _Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithmics and Combinatorics, ALENEX /ANALCO 2005, Vancouver, BC, Canada, 22 January 2005_. 218–221
  * Rapaport [1980] Rapaport, D. C. (1980).  The Event Scheduling Problem in Molecular Dynamic Simulation.  _Journal of Computational Physics_ 34, 184–201.  10.1016/0021-9991(80)90104-7
  * Sakai and Hukushima [2016] Sakai, Y. and Hukushima, K. (2016).  Eigenvalue analysis of an irreversible random walk with skew detailed balance conditions.  _Phys. Rev. E_ 93, 043318.  10.1103/PhysRevE.93.043318
  * Sinclair and Jerrum [1989] Sinclair, A. and Jerrum, M. (1989).  Approximate counting, uniform generation and rapidly mixing Markov chains.  _Information and Computation_ 82, 93–133.  10.1016/0890-5401(89)90067-9
  * Sugita and Okamoto [1999] Sugita, Y. and Okamoto, Y. (1999).  Replica-exchange molecular dynamics method for protein folding.  _Chemical Physics Letters_ 314, 141–151.  10.1016/s0009-2614(99)01123-9
  * Turitsyn et al. [2011] Turitsyn, K. S., Chertkov, M., and Vucelja, M. (2011).  Irreversible Monte Carlo algorithms for efficient sampling.  _Physica D: Nonlinear Phenomena_ 240, 410 – 414.  10.1016/j.physd.2010.10.003
  * Walker [1977] Walker, A. J. (1977).  An Efficient Method for Generating Discrete Random Variables with General Distributions.  _ACM Trans. Math. Softw._ 3, 253–256.  10.1145/355744.355749
  * Weber [2017] Weber, M. (2017).  Eigenvalues of non-reversible Markov chains – A case study.  ZIB report
  * Wegner [1967] Wegner, F. (1967).  Spin-ordering in a planar classical Heisenberg model.  _Zeitschrift für Physik_ 206, 465–470.  10.1007/BF01325702
  * Weigel [2018] Weigel, R. F. B. (2018).  Equilibration of orientational order in hard disks via arcuate event-chain Monte Carlo.  Master thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg
  * Wu et al. [2006] Wu, Y., Tepper, H. L., and Voth, G. A. (2006).  Flexible simple point-charge water model with improved liquid-state properties.  _The Journal of Chemical Physics_ 124, 024503.  10.1063/1.2136877
  * Xu et al. [2019] Xu, W., Sun, Y., Lv, J.-P., and Deng, Y. (2019).  High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class.  _Physical Review B_ 100\.  10.1103/physrevb.100.064525
  * Zhong and Marsden [1988] Zhong, G. and Marsden, J. E. (1988).  Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators.  _Physics Letters A_ 133, 134–139.  10.1016/0375-9601(88)90773-6