Statistical theory of nonequilibrium open systems

Abstract

A formal theory of nonequilibrium open systems is presented in the framework of the time-dependent projection operator. The theory is conducted in the Hilbert space ¢H S instead of in ¢H=¢H S⊗¢H R. It is shown that the influence of the environment on the open system is described by a separate non-Markovian term, which is determined by the interaction between the system and its environment. Two special cases that the environment is a thermal reservoir and that the environment deviates slightly from its initial equilibrium are discussed. In the former case, the non-Markovian term can be calculated by solving a Volterra equation, and in the latter case, by solving a hierarchy of equations of motion for a new kind of retarded two-time Green's functions.