Nonequilibrium Temperature for Open Boson and Fermion Systems

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 $T(t) = T_i(\bar{< \hat{H} (t) >_{\Psi}}/ \bar{< \hat{I} (t) >_{\Psi}})$, 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.