Andrieux David, Gaspard Pierre
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Mar;77(3 Pt 1):031137. doi: 10.1103/PhysRevE.77.031137. Epub 2008 Mar 28.
We report the analytical study of a class of chemical reactions described as birth-and-death stochastic processes ruled by a master equation compatible with the mass action law of chemical kinetics. We solve analytically this master equation to find the generating functions of the fluctuating fluxes and of the Lebowitz-Spohn action functional. These generating functions are explicitly shown to obey fluctuation theorems. In the case of fluxes, we derive relations for the nonlinear response coefficients, extending Onsager's reciprocity relations. Moreover, symmetry relations reminiscent of the fluctuation theorem are obtained for the finite-time probability distributions of the fluxes. The temporal disorder of the stochastic process is also characterized and related to the thermodynamic entropy production.
我们报告了一类化学反应的分析研究，这类反应被描述为由与化学动力学质量作用定律兼容的主方程所支配的生死随机过程。我们对这个主方程进行解析求解，以找到涨落通量和莱博维茨 - 施波恩作用泛函的生成函数。这些生成函数被明确证明服从涨落定理。对于通量的情况，我们推导了非线性响应系数的关系，扩展了昂萨格互易关系。此外，还得到了通量有限时间概率分布的类似于涨落定理的对称关系。随机过程的时间无序性也得到了表征，并与热力学熵产生相关。
