A Stochastic Extension of Macroscopic Stability Criterion of Nonequilibrium Steady State in Chemical Reaction Systems Governed by Master Equation

By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .