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Dynamical semigroups in the algebraic formulation of statistical mechanics
Author(s) -
Majewski W. A.
Publication year - 1984
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19840320302
Subject(s) - detailed balance , section (typography) , statistical mechanics , character (mathematics) , representation (politics) , algebraic number , mathematics , dynamical systems theory , balance (ability) , semigroup , pure mathematics , algebra over a field , calculus (dental) , statistical physics , mathematical analysis , computer science , physics , geometry , quantum mechanics , medicine , dentistry , politics , political science , law , physical medicine and rehabilitation , operating system
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.