  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.
