On the structure of the generalized master equation for open systems

A quantum open system S, interacting with a reservoir R is considered. The kernel of the generalized master equations (G.M.E.'s), usually deduced to describe the dynamics of S, is expressed in terms of time correlation functions of the bath operators involved in the interaction between S and R, calculated on a suitable equilibrium state of R. Such equilibrium state “enters” into the kernel in a rather artificial way, e.g. via the projection operator used to deduce the G.M.E. In this paper the structure of the kernel of the G.M.E. for open systems is justified from first principles, showing that the presence of the equilibrium state of R in the kernel arises in quite a natural way. The thermodynamic limit of R plays an essential role in connection with this result.