Nonequilibrium Temperature for Open Boson and Fermion Systems

Abstract

The effective theory of an open boson or fermion system is studied, which evolves out of equilibrium with time-dependent Hamiltonian $\hat{H}(t)$. A measure of nonequilibrium temperature for the open system evolving from an equilibrium is proposed as the time-averaged energy expectation value $T(t)=T_i(\overline{<\hat{H}(t){>}_{\Psi }}/\overline{<\hat{I}(t){>}_{\Psi }})$, where $\hat{I}(t)$, the action operator, satisfies the quantum Liouville-von Neumann equation and determines the true density operator. It recovers the result for the adiabatic (quasi-equilibrium) and nonadiabatic (out of equilibrium) evolution from one static Hamiltonian to another and takes into account the particle production due to the intermediate processes.

Comments: LaTex 11 pages, no figure; qualitative argument is added for the temperature relation of thermal equilibrium at high temperature and references are added