Abstract: A Criterion to identify the non-equilibrium chemical reaction systems at steady states departed from the detailed balance was constructed successfully at the stochastic level. Based on the Fokker-Planck equation, we have established a stochastic entropy balance equation for the non-equilibrium systems undergoing continuous Markov processes. Along with this balance we further decompose the time evolution of the stochastic entropy into two contributions in the stochastic state space: the stochastic entropy production and the conjugate flow. Furthermore, it has turned out that the stochastic entropy production in this formalism tends to trivial if the detailed balance is satisfied. Therefore, this kind of stochastic entropy production becomes an appropriate measure for the mesoscopic irreversibility departing from the detailed balance. By means of Ω-expansion it is shown that the stochastic entropy production remains to be a stochastic thermodynamic quantity in the order of N(N is an extensive quantity characteristic of the amount of system) originated from the irreversibility departing from the detailed balance, principally coming from the contribution of the non-Poisson fluctuations.

Key words: Fokker-Planck equation, Stochastic entropy production, Detailed balance, Non-poisson fluctuation, Stochastic force and stochastic flux