Nonequilibrium Physics Aspects of Probabilistic Cellular Automata

  • Christian MaesEmail author
Part of the Emergence, Complexity and Computation book series (ECC, volume 27)


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.


Nonequilibrium PCA Discrete time physics Minimum entropy production principle 


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Instituut voor Theoretische FysicaKU LeuvenLeuvenBelgium

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