  Parallel Kinetic Monte Carlo (KMC) is a potent tool to simulate stochastic
particle systems efficiently. However, despite literature on quantifying domain
decomposition errors of the particle system for this class of algorithms in the
short and in the long time regime, no study yet explores and quantifies the
loss of time-reversibility in Parallel KMC. Inspired by concepts from
non-equilibrium statistical mechanics, we propose the entropy production per
unit time, or entropy production rate, given in terms of an observable and a
corresponding estimator, as a metric that quantifies the loss of reversibility.
Typically, this is a quantity that cannot be computed explicitly for Parallel
KMC, which is why we develop a posteriori estimators that have good scaling
properties with respect to the size of the system. Through these estimators, we
can connect the different parameters of the scheme, such as the communication
time step of the parallelization, the choice of the domain decomposition, and
the computational schedule, with its performance in controlling the loss of
reversibility. From this point of view, the entropy production rate can be seen
both as an information criterion to compare the reversibility of different
parallel schemes and as a tool to diagnose reversibility issues with a
particular scheme. As a demonstration, we use Sandia Lab's SPPARKS software to
compare different parallelization schemes and different domain (lattice)
decompositions.
