The Green-Kubo formula, autocorrelation function and fluctuation spectrum for finite Markov chains with continuous time

摘要

A general form of the Green-Kubo formula, which describes the fluctuations pertaining to all the steady states whether equilibrium or non-equilibrium, for a system driven by a finite Markov chain with continuous time (briefly, MC)({xi(1)}, is shown. The equivalence of different forms of the Green-Kubo formula is exploited. We also look at the differences in terms of the autocorrelation function and the fluctuation spectrum between the equilibrium state and the non-equilibrium steady state. Also, if the MC is in the non-equilibrium steady state, we can always find a complex function p, such that the fluctuation spectrum of {p(xi(1))} is non-monotonous in [0,+infinity).