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On the inverse problem of statistical physics: from irreversible semigroups to chaotic dynamics

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  • Antoniou, I.
  • Gustafson, K.
  • Suchanecki, Z.

Abstract

We show that all measure preserving stationary Markov processes arise as projections of Kolmogorov dynamical systems which have positive entropy production and are prototypes of chaos. This result not only contributes to the clarification of the relation of dynamics with stochastic processes but also shows the physical significance of the Misra–Prigogine–Courbage theory of irreversibility in the more general context of the inverse problem of statistical physics. 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. & 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.
    • Handle: RePEc:eee:phsmap:v:252:y:1998:i:3:p:345-361
    DOI: 10.1016/S0378-4371(97)00622-5
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    References listed on IDEAS

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    1. Misra, B. & Prigogine, I. & Courbage, M., 1979. "From deterministic dynamics to probabilistic descriptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 1-26.
    2. 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.
    3. -, 1976. "Información general y programa de trabajo 1976," Sede de la CEPAL en Santiago (Estudios e Investigaciones) 29163, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    4. Goodrich, K. & Gustafson, K. & Misra, B., 1980. "On converse to Koopman's Lemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(2), pages 379-388.
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