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Event-Chain Monte Carlo methods generate continuous-time and non-reversibleMarkov processes which often display important accelerations compared to theirreversible counterparts. However their generalization to any system may appearless straightforward. In this work, we build on the recent analyticalcharacterization of such methods as generating Piecewise Deterministic MarkovProcesses (PDMP) to clearly decipher the necessary symmetries the PDMP mustobey from the sufficient ones which may prove to be too restrictive in ageneral setting. Thus, we derive a necessary rotational invariance of theprobability flows and the minimum event rate, which identifies with thecorresponding infinitesimal rejection rate. Such conditions always yield acorrect ECMC scheme. We then generalize such results to the case of moregeneral deterministic flows than the translational ones. In particular, wedefine two classes of interest of general flows, the ideal and uniform-idealones, which respectively suppresses or reduces the event rates. From there, weimplement a complete non-reversible sampling of a systems of hard dimers,thanks to the introduction of rotational flows, which are uniform-ideal andshows a speed-up of up to ~3 compared to the state-of-the-art ECMC/Metropolishybrid scheme.

Necessary and sufficient symmetries in Event-Chain Monte Carlo with generalized flows and Application to hard dimers