Abstract
We consider shift-invariant probability measures on subshift dynamical systems with a transition matrixA which satisfies the Chapman-Kolmogorov equation for some stochastic matrix Π compatible withA. We call them Chapman-Kolmogorov measures. A nonequilibrium entropy is associated to this class of dynamical systems. We show that ifA is irreducible and aperiodic, then there are Chapman-Kolmogorov measures distinct from the Markov chain associated with Π and its invariant row probability vectorq. If, moreover, (q, Π) is a reversible chain, then we construct reversible Chapman-Kolmogorov measures on the subshift which are distinct from (q, Π).
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