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 TMF, 1975, Volume 25, Number 1, Pages 10–19 (Mi tmf4030)

Nonautomorphic dynamics in algebraic statistical mechanics

V. M. Maksimov

Abstract: The scheme of the nonautomorphic dynamics in the algebraic statistical mechanics is proposed, which is based on the Heisenberg equations defined on algebras of microscopic observables. In contrast to the case of the automorphic dynamics these equations are not supposed to have the solutions in the algebra. The Liouville equations in the space of states are determined by the Heisenberg equations. General properties of the solutions of Liouville equations are investigated on certain sets of states, which we name quasi-equilibrium states. It is shown that the macroscopic causality principle is valid for the quasi-equilibrium states and in the representations determined by physically pure invariant states the dynamics is generated by the spatial group of automorphisms of the weak closure of the microscopic observable algebra.

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English version:
Theoretical and Mathematical Physics, 1975, 25:1, 944–943

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Citation: V. M. Maksimov, “Nonautomorphic dynamics in algebraic statistical mechanics”, TMF, 25:1 (1975), 10–19; Theoret. and Math. Phys., 25:1 (1975), 944–943

Citation in format AMSBIB
\Bibitem{Mak75} \by V.~M.~Maksimov \paper Nonautomorphic dynamics in algebraic statistical mechanics \jour TMF \yr 1975 \vol 25 \issue 1 \pages 10--19 \mathnet{http://mi.mathnet.ru/tmf4030} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=489595} \zmath{https://zbmath.org/?q=an:0374.46052} \transl \jour Theoret. and Math. Phys. \yr 1975 \vol 25 \issue 1 \pages 944--943 \crossref{https://doi.org/10.1007/BF01037636} 

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This publication is cited in the following articles:
1. V. M. Maksimov, “Dynamics in the state space and Heisenberg equations”, Theoret. and Math. Phys., 26:3 (1976), 259–262
2. V. M. Maksimov, “Heisenberg dynamics. Covariant representations”, Theoret. and Math. Phys., 28:2 (1976), 715–720
3. V. M. Maksimov, “On the existence of the Heisenberg equations on the $C^*$ algebra of quasilocal observables of bose and fermi systems with a finite-range potential”, Theoret. and Math. Phys., 31:1 (1977), 371–373
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