Résumé
“All known life forms are based on self-propelled entities uniting to create large-scale structures andmovements. If this didn’t happen, organisms would be limited to using much slower, passive processes suchas diffusion to move DNA and proteins around inside cells or tissues, and many of life’s complex structuresand functions might never have evolved.”[1] A central question in the field of active matter concerns theemergent collective phenomena when individual particles have the ability to move persistently, i.e. whenparticles overcome a characteristic finite distance without changing their direction of motion. Althoughconsiderable effort has been put to develop analytical approaches to describe the statistical physics ofactive matter, the state of the art is far from comparable approaches in equilibrium statistical physics.Our advances therefore mainly rely on numerical studies where many active-matter models have beenproposed and simulated. However, little attempts have been made to develop an algorithmic toolbox forthose models. In equilibrium, the detailed-balance condition allows to exploit the unphysical moves ofMonte Carlo (MC) approaches to efficiently simulate large systems. As there is no analog of detailedbalance for active matter, the construction of MC algorithms that faithfully capture continuous-timeactive-matter models is not straight forward. I will present a realisation of kinetic MC analogues of thework-horse models of self-propelled particles, namely Active-Ornstein Uhlenbeck, Active Brownian, andRun-and-Tumbles particles.[2][1] G. Popkin The physics of life. Nature, 529, 16–18, 2016.[2] J. U. Klamser, O. Dauchot, J. Tailleur Kinetic Monte Carlo Algorithms for Active Matter SystemsPhys. Rev. Lett., 127, 150602, 2021.