Abstract
A stochastic model of chemical reaction-heat conduction-diffusion for a one-dimensional gaseous system under Dirichlet or zero-fluxes boundary conditions is proposed in this paper. Based on this model, we extend the theory of the broadening exponent of critical fluctuations to cover the chemical reaction-heat conduction coupling systems as an asymptotic property of the corresponding Markovian master equation (ME), and establish a valid stochastic thermodynamics for such systems. As an illustration, the non-isothermal and inhomogeneous Schlogl model is explicitly studied. Through an order analysis of the contributions from both the drift and diffusion to the evolution of the probability distribution in the corresponding Fokker-Planck equation(FPE) in the approach to bifurcation, we have identified the critical transition rule for the broadening exponent of the fluctuations due to the coupling between chemical reaction and heat conduction. It turns out that the dissipation induced by the critical fluctuations reaches a deterministic level, leading to a thermodynamic effect on the nonequilibrium physico-chemical processes.
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