Maes, Christian. “Nonequilibrium physics aspects of probabilistic cellular automata.” In Probabilistic Cellular Automata , pp. 119-128. Springer, Cham, 2018.
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Probabilistic cellular automata (PCA) are used to model a variety of discrete spatially extended systems undergoing parallel-updating. We propose an embedding of a number of classical nonequilibrium concepts in the PCA-world. We start from time-symmetric PCA, satisfying detailed balance, and we give their Kubo formula for linear response. Close-to-detailed balance we investigate the form of the McLennan distribution and the minimum entropy production principle. More generally, when time-symmetry is broken in the stationary process, there is a fluctuation symmetry for a corresponding entropy flux. For linear response around nonequilibria we also give the linear response which is now not only entropic in nature.