Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-01-25
Phys. Lett. A 375 (2011) 2797-2801
Physics
Condensed Matter
Statistical Mechanics
Latex file, 11 pages
Scientific paper
An isolated quantum system is considered, prepared in a nonequilibrium initial state. In order to uniquely define the system dynamics, one has to construct a representative statistical ensemble. From the principle of least action it follows that the role of the evolution generator is played by a grand Hamiltonian, but not merely by its energy part. A theorem is proved expressing the commutators of field operators with operator products through variational derivatives of these products. A consequence of this theorem is the equivalence of the variational equations for field operators with the Heisenberg equations for the latter. A finite quantum system cannot equilibrate in the strict sense. But it can tend to a quasi-stationary state characterized by ergodic averages and the appropriate representative ensemble depending on initial conditions. Microcanonical ensemble, arising in the eigenstate thermalization, is just a particular case of representative ensembles. Quasi-stationary representative ensembles are defined by the principle of minimal information. The latter also implies the minimization of an effective thermodynamic potential.
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