Abstract
The conditions for mapping chaotic dynamics into a Markov chain through finite coarse-graining are derived. A Chapman-Kolmmogorov equation giving rise to an H-theorem is deduced, in which the transition probability matrix is expressed entirely in terms of the properties of the underlying deterministic dynamics and of the phase-space partition. The validity of the conditions ensuring the mapping is verified on simple models of dissipative as well as conservative dynamical systems. The implications of the results in the problem of irreversibility and the relation between deterministic chaos, information and complexity are discussed.
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