Derivation of Generalized Master Equations

Abstract

We present a simplified derivation of a generalized master equation for the diagonal part of the occupation probability density. This derivation is valid for systems of arbitrary volume. It does not require the use of perturbation expansions nor the use of a diagonal singularity condition. In addition, a similar derivation is presented of a generalized master equation for the nondiagonal part of the occupation probability density. These equations become identical to the generalized master equations of Van Hove and Janner, respectively, if a perturbation expansion is made, if a diagonal singularity condition is assumed, and if the limit of infinite volume is taken.