Effects of critical fluctuations to stochastic thermodynamic behavior of chemical reaction systems at steady state far from equilibrium

We extend the stochastic thermodynamics of chemical reaction systems to include the critical regime. An explicit theory of stochastic entropy production valid for the fluctuations around non-equilibrium steady state with broadening exponent alpha = 3/4 is presented in this paper. It is shown that the contribution of this critical fluctuations to entropy production tends to the order of V-1/2 (where V is the volume of the system), mainly consisting of two parts due respectively to the deviations of the distribution from Poissonian behavior and the central limit theorem. Furthermore, it is found that the stochastic average of 2nd order excess entropy production due to internal fluctuations is linked to the entropy production of the critical fluctuations. In this regime of the distribution it is possible to detect the macroscopic stability of chemical reaction systems at steady state by means of a general analysis of the fluctuation behaviour.