Master Equations and Markov Processes

Abstract

The processes described by generalized master equations (GME), derived from the Liouville equation on the basis of various physical and dynamic arguments, have been termed Markovian or non-Markovian depending upon whether the GME did not or did involve an explicit time integration. We show that these designations are not in accord with the (very specific) mathematical definitions of Markovian and non-Markovian processes. We demonstrate that the GME does not contain sufficient information to determine whether or not the stochastic process described by it is Markovian or non-Markovian.