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Moscow Mathematical Journal

Volume 20, Issue 4, October–December 2020  pp. 813–816.

What is Time Reversal?

Authors:  E.N. Petrova (1) and S.A. Pirogov (1)
Author institution:(1) Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia


We analyze the concept of time reversibility in the quantum and in the classical context, including Markov processes. It turns out that in many cases the physical reversibility is equivalent to the existence of a bilinear form with respect to which the evolution operator is symmetric.

2010 Math. Subj. Class. 60K40.

Keywords: One-parameter semigroup, reversibility, CPT-invariance.

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