Abstract
The image of Dirac measures τx by the operator Λ of the construction of Prigogine and collaborators is shown to be concentrated in the stable manifold Xst(x) and its density function ρ is studied for Bernoulli shifts. The valuev ∞ = exp[−h μ (T)], whereh μ (T) is the Kolmogorov entropy, appears as a critical point for the behavior of ρ. It is also proved that no loss of information is involved by passing from the dynamical system to the Markov process when vx > 1/2. The discussion is based on the introduction of an invariant for Markov systems that generalizes the usual Kolmogorov entropy for dynamical systems.
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Martinez, S., Tirapegui, E. The role of stable manifolds and information in the Prigogine theory of irreversibility. J Stat Phys 48, 1283–1294 (1987). https://doi.org/10.1007/BF01009546
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DOI: https://doi.org/10.1007/BF01009546