The physics of active matter is determined by the non-equilibrium dynamics of the constituent particles. While constructing a non-equilibrium Monte Carlo (MC) dynamics for active matter is straightforward, the question remains to what extent this discrete-time dynamics faithfully captures real-world/continuous-time active systems. We focus on a kinetic MC version for the simplest kind of active matter: persistently moving, non-polar, interacting particles. On the multi-particle level, the MC dynamics captures not only Motility-induced phase separation [1] but also features a non-equilibrium extension of the celebrated two-dimensional melting [2]. We show [3], however, that the continuous-time limit of existing MC dynamics[1,2] is ill-defined, leading to the vanishing of trademark behaviours of active matter such as the motility-induced phase separation, ratchet effects, as well as to a diverging mechanical pressure. We show [3] how mixing passive/uncorrelated moves with active/time-correlated ones regularises this behaviour, leading to a well-defined continuous-time limit. We propose new active kinetic MC algorithms whose continuous-time limits are the Langevin descriptions of the work-horse active-matter models, namely Active-Ornstein Uhlenbeck, Active Brownian, and Run-and-Tumbles particles.

References:

[1] D. Levis and L. Berthier, Phys. Rev. E 89 (2014), 062301

[2] J. U. Klamser, S. C. Kapfer and W. Krauth, Nat Commun 9 (2018) 5045

[3] J. U. Klamser, O. Dauchot and J. Tailleur, Phys. Rev. Lett. 127 (2021), 150602