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Nonlocality of the Misra-Prigogine-Courbage semigroup

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Abstract

We show that the Markov semigroups constructed by Misra, Prigogine, and Courbage through nonunitary similarity transformations of Kolmogorov systems are not implementable by local point transformations, i.e., they are not the Frobenius-Perron semigroups associated with noninvertible point transformations, in contrast with the semigroups obtained by coarse-graining projections. Our result is a straightforward generalization of the proof of the nonlocality of the similarity transformation given by Goldstein, Misra, and Courbage and also of the previous illustration by Misra and Prigogine for the baker transformation and completes the characterization of the Misra-Prigogine-Courbage semigroups.

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Authors and Affiliations

  1. International Solvay Institutes for Physics and Chemistry, 1050, Brussels, Belgium

    Z. Suchanecki, I. Antoniou & S. Tasaki

  2. Hugo Steinhaus Center and Institute of Mathematics, Wroclaw Technical University, Wroclaw, Poland

    Z. Suchanecki

  3. Theoretische Natuurkunde, Free University of Brussels, 1050, Brussels, Belgium

    I. Antoniou

Authors
  1. Z. Suchanecki
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  2. I. Antoniou
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  3. S. Tasaki
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Suchanecki, Z., Antoniou, I. & Tasaki, S. Nonlocality of the Misra-Prigogine-Courbage semigroup. J Stat Phys 75, 919–928 (1994). https://doi.org/10.1007/BF02186750

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  • DOI: https://doi.org/10.1007/BF02186750

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