Thermodynamically Equivalent Hamiltonian Method in Nonequilibrium Statistical Mechanics
Marvin D. Girardeau
The equilibrium statistical mechanics of the Bardeen-Cooper-Schrieffer model of superconductivity, as well as that of a wide class of similar models, can be evaluated exactly by the ``thermodynamically equivalent Hamiltonian'' method of Bogoliubov, Zubarev, Tserkovnikov, and Wentzel. It has been pointed out by Wentzel that this method can be extended to certain weakly nonequilibrium situations. It is shown here that the method allows an exact evaluation of the nonequilibrium statistical mechanics of the following situations: (a) temporal evolution of the statistical expectation value of an observable O(r) whose initial deviation from equilibrium is spatially localized, but not necessarily small; (b) temporal evolution of the statistical expectation value of an observable O due to a perturbation V which is spatially localized, but not necessarily small.
Journal of Mathematical Physics•Mar 1, 1967•5 citations