  We propose an information-theoretic approach to analyze the long-time
behavior of numerical splitting schemes for stochastic dynamics, focusing
primarily on Parallel Kinetic Monte Carlo (KMC) algorithms.Established methods
for numerical operator splittings provide error estimates in finite-time
regimes, in terms of the order of the local error and the associated
commutator. Path-space information-theoretic tools such as the relative entropy
rate (RER) allow us to control long-time error through commutator calculations.
Furthermore, they give rise to an a posteriori representation of the error
which can thus be tracked in the course of a simulation. Another outcome of our
analysis is the derivation of a path-space information criterion for comparison
(and possibly design) of numerical schemes, in analogy to classical information
criteria for model selection and discrimination. In the context of Parallel
KMC, our analysis allows us to select schemes with improved numerical error and
more efficient processor communication. We expect that such a path-space
information perspective on numerical methods will be broadly applicable in
stochastic dynamics, both for the finite and the long-time regime.
