Dynamical semigroups in the algebraic formulation of statistical mechanics

The paper summarizing the recent results of the author is devoted to a detailed analysis of positive semigroups appearing in dynamical description of non-equilibrium statistical mechanics. The first part of paper has a review character (this goes especially to sections 1 and 2). Novel aspects are contained in sections 3, 4 and 5. Section 4 contains the formulation and relatively complete discussion of detailed balance condition. In particular, the representation theorem for dynamical semigroups satisfying detailed balance is given. Section 5 contains new results from the theory of strongly and strictly positive semigroups.

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