化学反应-传热耦合体系中涨落展布指数的临界突跃律及其对耗散的效应

Critical transition rule of broadening exponent of fluctuation and its affection on dissipation in chemical reaction-heat conduction coupling systems

建立了在Dirichlet或零流边界条件下一维气体化学反应-传热-扩散耦合系统的随机模型,并以此为基础,推广了以Fokker-Plank方程为基础的临界涨落量级分析理论,并进一步建立了该类体系的随机热力学.同时,以非等温非均匀Schlogl模型体系为例,通过对相应的Fokker-Plank方程中漂移及扩散对概率分布演化之贡献的量级分析,论证了受制于化学反应-传热耦合的涨落展布指数的临界突跃律;发现临界涨落导致的耗散(涨落熵产生)已达决定性层次,不可避免将通过其热力学效应影响该类系统中进行的物理化学过程.

A stochastic model of chemical reaction-heat conduction-diffusion for a one-dimensional gaseous system under Dirichlet or zero-fluxesboundary 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.