Copyright © 2010 Hidetoshi Konno. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

There are two types of master equations in describing nonequilibrium phenomena with memory effect: (i) the memory function type and (ii) the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transition-rate with an arbitrary time-dependent relaxation function, the exact solution of a generalized Polya process is obtained. The characteristic features of temporal variation of the solution are displayed for some typical time-dependent relaxation functions reflecting memory in the systems.