Stochastic thermodynamics of nonequilibrium steady states in chemical reaction systems

We present a stochastic theory of entropy production for steady states in chemical reaction systems. Small scale internal fluctuations around steady states are considered in the Gaussian regime. It is shown that in addition to the usual Gibbsian form of entropy production, there is an entropy production due to fluctuation which is of order O(V⁰). This comes from the non-Poisson character of the probability distribution in a nonequilibrium system. Two approaches are considered: in the first, we use an entropy balance equation based on the master equation; in the second, we use a stochastic potential related to the probability distribution and built from the generalized Einstein relation. We show that both approaches give the same result for the entropy production of fluctuation (diS/dt)_f. Next we consider a simple one-component nonequilibrium system under the perturbation of a macroscopically large external fluctuation as a power generator. We interpret (diS/dt)_f in terms of net power gain factor under random external fluctuations in the spirit of a generalized "fluctuation-dissipation" theorem. It is shown that positive power gain is possible only for system staying far enough from equilibrium.