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A critical transition rule for broadening exponent of fluctuation and its effect on dissipation in chemical reaction-heat conduction coupling systems

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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 Schlögl 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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Authors and Affiliations

  1. Institute of Chemical Physics, College of Chemistry, Sichuan University, Chengdu, 610064, China

    Feng Lin, NanRong Zhao & JiuLi Luo

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  1. Feng Lin
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  2. NanRong Zhao
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  3. JiuLi Luo
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Correspondence to NanRong Zhao or JiuLi Luo.

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Lin, F., Zhao, N. & Luo, J. A critical transition rule for broadening exponent of fluctuation and its effect on dissipation in chemical reaction-heat conduction coupling systems. Sci. China Chem. 54, 774–781 (2011). https://doi.org/10.1007/s11426-011-4254-6

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  • DOI: https://doi.org/10.1007/s11426-011-4254-6

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