鉴于用主方程法处理反应–扩散–传热耦合系统涨落分布面临求解含有超越函数系数之概率微分方程的数学解析困难，在该项目执行后期彻底改变理论方法，发展和推广了涨落沿决定性路径展布指数的概念，以Fokker–Planck 方程为依据进一步建立了求解三类耗散过程耦合共存系非平衡稳态涨落展布指数的系统理论及算法体系。同时，在建立传热过程随机模型的基础上，推广了等温化学反应系统的随机热力学，最终完满解决了统计解析该类系统非平衡涨落–耗散的热力学效应，及其对非平衡物理化学过程的影响的任务。已经阐明：（1）在传热系统及传热–扩散系统中，温度–浓度（或密度）涨落的展布指数始终为1/2, 受制于Gauss分布律。此时涨落导致的耗散及其热力学效应低于宏观量级；（2）如果化学反应与传热–扩散共存，由于反应速度与温度相关三类过程必产生定态耦合，在外控状态接近分支点快于热力学极限的条件下温度–浓度涨落将跨越Gauss区进入临界区，展布指数可跃迁至大于3/4，接近于1的程度。在此情况下，热力学效应逼近宏观量级，对物理化学过程将产生影响。以分析化学反应–传热系涨落对稳定性的影响为范例，已建立应用基础理论框架。

To get rid of the difficulty in solving the probabilistic differential equation with transcendental functions coefficients for analysis of the fluctuation arising in the chemical reaction-diffusion-heat conduction systems by master equation, we have developed the concept of broaden exponent of the fluctuation along deterministic path in thermodynamic limit by means of the Fokker-Planck equation. Furthermore, a systematic theory together with a complete algorithm for solving the broaden exponent of fluctuations around the non-equilibrium steady states of chemical reaction-diffusion-heat conduction systems have been also established. Simultaneously, based on the stochastic model of the heat conduction we have generalized the stochastic thermodynamics of chemical reaction systems to include the non-isothermal cases. Then the task to reveal the statistical contents of the thermodynamic effects from fluctuation-dissipation arising in this kind of systems has been fulfilled successfully. It turns out that (1) For both pure heat conduction systems and heat conduction-diffusion systems the broaden exponents of the fluctuations of temperature-concentration (or density) keep to be 1/2, dominated by the Gaussian distribution. In this case the order of the fluctuation and its thermodynamic effects is negligibly lower than macroscopic level. (2) For the chemical reaction-diffusion-heat conduction systems the 3 kinds of dissipative processes will be coupled avoidably at steady states because of the relation between reaction rate and temperature. As a result the distribution of the fluctuation of temperature-concentration will cross the Gauss regime into a critical regime with broaden exponent higher than 3/4 tending to 1 if the externally controlled constraints tend to bifurcation point rapidly than the thermodynamic limit. In such a case the thermodynamic effects on the physico-chemical processes from the fluctuation-dissipation in the non-isothermal chemical reaction systems will rise to the macroscopic level. As an illustration, a basic theory applicable for analyzing the macroscopic stability affected by the fluctuation in chemical reaction-heat conduction systems has been established. It is also capable of using to revise the phenomenological calculation of the stability region.

鉴于用主方程法处理反应–扩散–传热耦合系统涨落分布面临求解含有超越函数系数之概率微分方程的数学解析困难，在该项目执行后期彻底改变理论方法，发展和推广了涨落沿决定性路径展布指数的概念，以Fokker–Planck 方程为依据进一步建立了求解三类耗散过程耦合共存系非平衡稳态涨落展布指数的系统理论及算法体系。同时，在建立传热过程随机模型的基础上，推广了等温化学反应系统的随机热力学，最终完满解决了统计解析该类系统非平衡涨落–耗散的热力学效应，及其对非平衡物理化学过程的影响的任务。已经阐明：（1）在传热系统及传热–扩散系统中，温度–浓度（或密度）涨落的展布指数始终为1/2, 受制于Gauss分布律。此时涨落导致的耗散及其热力学效应低于宏观量级；（2）如果化学反应与传热–扩散共存，由于反应速度与温度相关三类过程必产生定态耦合，在外控状态接近分支点快于热力学极限的条件下温度–浓度涨落将跨越Gauss区进入临界区，展布指数可跃迁至大于3/4，接近于1的程度。在此情况下，热力学效应逼近宏观量级，对物理化学过程将产生影响。以分析化学反应–传热系涨落对稳定性的影响为范例，已建立应用基础理论框架。