  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 appropriate formula which is now not only
entropic in nature.
