On the Decay of Initial Correlations in Stochastic Processes

We study the relaxation of a noninteracting, initially correlated many-particle system in contact with an infinite reservoir. We use the master equation to study the time development of the r-particle distribution function Pr(n;t) and assume that the relaxation process is Markovian. We study the decay of the correlations by investigating the time development of the r-particle Ursell functions, Ur(n;t). We show that the correlation function Ur(n;t) goes to zero much more rapidly with time than the r-particle distribution function approaches its equilibrium value Pr(n; ∞)=Π lim i=1rP(ni; ∞).The exact forms of the relaxation of Pr(n;t) and Ur(n;t) depend upon the eigenvalue spectrum of the transition rate matrix of the master equation. The general theory is developed and then applied to a number of examples.