Information Criteria for quantifying loss of reversibility in   parallelized KMC
  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. 
Konstantinos Gourgoulias, Markos A. Katsoulakis, Luc Rey-Bellet
math.NA cs.IT math.IT