Nonautomorphic dynamics in algebraic statistical mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 1, pp. 10-19
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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.
@article{TMF_1975_25_1_a1,
author = {V. M. Maksimov},
title = {Nonautomorphic dynamics in algebraic statistical mechanics},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {10--19},
publisher = {mathdoc},
volume = {25},
number = {1},
year = {1975},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1975_25_1_a1/}
}
V. M. Maksimov. Nonautomorphic dynamics in algebraic statistical mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 1, pp. 10-19. http://geodesic.mathdoc.fr/item/TMF_1975_25_1_a1/