  Event-Chain Monte Carlo methods generate continuous-time and non-reversible
Markov processes which often display important accelerations compared to their
reversible counterparts. However their generalization to any system may appear
less straightforward. In this work, we build on the recent analytical
characterization of such methods as generating Piecewise Deterministic Markov
Processes (PDMP) to clearly decipher the necessary symmetries the PDMP must
obey from the sufficient ones which may prove to be too restrictive in a
general setting. Thus, we derive a necessary rotational invariance of the
probability flows and the minimum event rate, which identifies with the
corresponding infinitesimal rejection rate. Such conditions always yield a
correct ECMC scheme. We then generalize such results to the case of more
general deterministic flows than the translational ones. In particular, we
define two classes of interest of general flows, the ideal and uniform-ideal
ones, which respectively suppresses or reduces the event rates. From there, we
implement a complete non-reversible sampling of a systems of hard dimers,
thanks to the introduction of rotational flows, which are uniform-ideal and
shows a speed-up of up to ~3 compared to the state-of-the-art ECMC/Metropolis
hybrid scheme.
