Abstract
Here we give the proof of a general theorem concerning irreversibility that was stated earlier by Misra and Prigogine. In terms of a unitary group describing a deterministic dynamical evolution and a related Markov semigroup describing an associated coarse grained probabilistic evolution, it is shown that the original dynamics are necessarily those of aK flow. Thus a reversible dynamics which permits such an intertwining to an irreversible description must possess a high degree of instability.
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This research was partially supported by NATO grant 889/83.
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Goodrich, R.K., Gustafson, K. & Misra, B. OnK-flows and irreversibility. J Stat Phys 43, 317–320 (1986). https://doi.org/10.1007/BF01010584
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DOI: https://doi.org/10.1007/BF01010584