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From irreversible Markov semigroups to chaotic dynamics

Author

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  • Antoniou, I.
  • Gustafson, K.

Abstract

We answer qualitatively the inverse coarse-graining problem of statistical physics, namely, which microscopic dynamics give rise to a given physically observed Markov semigroup as a result of exact coarse graining? We prove the fact that all Markov chains arise as projections of dynamical systems in larger spaces and show that in particular the irreversible Markov chains arise as projections of chaotic systems of Kolmogorov type. This result generalizes our previous results on the Misra-Prigogine-Courbage semigroups. Because we want positivity-preserving transformations, our procedure although analogous to the Sz-Nagy-Foias dilation theory has a different viewpoint, that of positive dilations.

Suggested Citation

  • Antoniou, I. & Gustafson, K., 1997. "From irreversible Markov semigroups to chaotic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 236(3), pages 296-308.
    • Handle: RePEc:eee:phsmap:v:236:y:1997:i:3:p:296-308
    DOI: 10.1016/S0378-4371(96)00375-5
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    References listed on IDEAS

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    1. Courbage, M. & Coutsomitros, C.Th. & Misra, B., 1989. "Faithfulness property of the transition from Bernoulli systems to irreversible Markov processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 155(1), pages 167-174.
    2. Jing-Yee, Lee & Tasaki, S., 1992. "Poincaré's theorem and subdynamics for driven systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(1), pages 59-99.
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    Cited by:

    1. Antoniou, I. & Gustafson, K. & Suchanecki, Z., 1998. "On the inverse problem of statistical physics: from irreversible semigroups to chaotic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 252(3), pages 345-361.

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