受高斯白噪声影响的有限化学反应体系的随机热力学——外噪声对化学反应体系影响的有效热力学量度

通过分析噪声对跃迁概率的不同影响,借助Novikov定理及MSR理论,建立了受多源白噪声影响的有限化学反应体系的有效主方程及有效熵平衡方程,导出非平衡定态时这类噪声体系熵产生的一般表达式,揭示涨落熵产生的统计内涵及噪声贡献,并针对非宏观量级的外噪声,借助扰动按分布参数分离法及有效主方程的Kramers-Moyal展开,进一步对简单加合性噪声建立了非平衡定态宏观稳定性判据的随机模拟,论证了噪声对化学反应体系定态稳定性的弱化作用.     

受主方程控制的化学反应体系非平衡定态宏观稳定性判据之随机推广

借助扰动按分布参数分离法及主方程的Kramers-Moyal展开证明,随机熵相应于对最可几路径偏离的偏超量之时间导数与体系对外部扰动的响应性直接相关.该演变速率等价于偏超随机熵产生,并与根据随机位方法提出的随机超熵产生速率等效.对Poisson分布,该量表现为Gibbs超熵产生的等价量.局域平衡假定失效后,化学反应体系的宏观稳定性即决定于这个新的随机量.     

对流扩散传质滞后的电极过程中之非Poisson涨落与非Nernst浓度极化

根据对流扩散传质滞后的恒稳电极过程中边界层的物理图像, 提出了该类电极过程的简化随机模型, 建立了相应的浓度极化的随机热力学理论, 揭示了非Nernst浓度极化来自于随电流密度增大电极化学反应体系涨落分布的非Poisson化与对中心极限律的偏离, 进一步阐明了与滞后的扩散步骤共存的对流传质对非Nernst浓度极化的效应及其规律. 同时, 给出了对流引起的非Nernst浓度极化的随机热力学算例.     

苯酚+环己酮固液平衡的热力学计算

对苯酚+环己酮低温固液平衡体系,直接由相图和基本热力学数据,计算体系热力学性质。使用Gibbs-Duhem方程和四参量GE方程,在220.00～241.00K区间,计算了8个温度的两组元活度系数和GE方程,在241.00K,x2=0.5、GE=783.69J/mol,SE=97.11/(mol.K),HE=24186.69J/mol。241.00K相合熔点化合物的离解平衡ΔrGm=1982.93J/mol,ΔrHm=5753.241J/mol,ΔrSm=15.65J/(mol.K)。体系偏离于规则溶液模型。在化合物存在相区,离解反应的反应焓变和熵变均可视之为常量。液相区不会存在稳定的化合物。     

精馏节能过程非平衡热力学分析——模型方程的建立

通过对精馏过程进行热力学分析,建立了通用性较强的非平衡热力学数学模型.该模型可对精馏过程中用能情况进行非平衡热力学分析和熵均分分析,也可用于评价塔板性能.模型建立的基础只适用于线性非平衡热力学区,即近平衡区,有较大的局限性.     

非恒稳含时电极过程中涨落-耗散的电化学效应——恒电势滴汞电极体系的随机热力学模型

以滴汞电极体系为模型,对非恒稳恒电势动态不可逆电极过程中的耗散-涨落效应进行了系统的研究.基于滴汞电极体系的电化学特征,提出了一个简化的含时随机热力学模型,从而可能对这类重要的含时物理化学过程进行涨落和耗散的定量分析.借助该简化的模型,成功地建立了恒电势滴汞电极过程的基本随机热力学公式,由此推出耗散-涨落效应的理论极谱曲线.在滴汞电极生长缓慢及扩散步骤严重滞后情况下,含时的滴汞电极过程将趋于在有效扩散层厚度演化的慢流型上的准定态过程.在这种准定态近似下,具体分析了涨落对极谱曲线的影响.结果表明,在涨落影响可以忽略的近平衡区,从耗散-涨落导出的极谱方程与从平衡态Nernst公式导出的极谱方程完全吻合.还计算了一个涨落诱导的极谱曲线偏离的典型范例.     

由细致平衡、质量守恒看速度常数和平衡常数及基元反应和总反应的关系

细致平衡原理表明,反应体系处于平衡时,每一基元反应的速度一定与其逆反应的速度相等。细致平衡原理可通过量子力学的微观可逆性和热力学第二定律来论证说明。依据细致平衡原理可从反应机理导出由诸基元反应速度常数表达的平衡常数。质量守恒原理应用在化学反应中,表现为假设的反应机理必存在一系列的质量守恒条件,以此得到反应前后原子(原     

对"燃料电池物理及化学性能的有限时间热力学分析法”的讨论

近期在本刊发表的"燃料电池物理及化学性能的有限时间热力学分析法”一文[1],将近20多年来新发展的有限时间热力学理论用于化学过程的研究,是很有意义的,特别是在研究中考虑了化学反应不可逆性和传热不可逆性,更值得提倡和重视.但文献[1]的结果是不正确的,主要对系统和有关环境的总熵产生率计算有问题,概念上有错误.     

关于"对‘燃料电池物理及化学性能的有限时间热力学分析方法'的讨论”答复

把有限时间热力学理论用于化学过程的研究,将会得到一系列新的结论,开展这方面的研究是很有意义的.文献[1]以燃料电池为例,在同时考虑化学反应及传热不可逆性的情况下,研究了燃料电池的性能界限,文献[2]指出了文献[1]计算化学反应及传热不可逆性而引起系统与有关环境的总熵产生率的错误以及由此而导致的结论所存在的问题,并进行了富有启发性的分析与讨论.但文献[2]对于系统与有关环境的总熵产生率的计算也是不正确的,由此得到的其它结论自然不能成立.本文将就此情况下系统与有关环境的总熵产生率的计算再次进行讨论,并给出电池功率和效率的有限时间热力学性能界限.     

非平衡化学反应的热力学

化学现象是由反应速率表征的,只有在非平衡条件下化学反应过程才会呈现出非零的反应速率.因此化学现象本身是一种非平衡现象,化学热力学应属于非平衡态热力学(也称不可逆过程热力学)的范畴.但是传统的化学热力学主要限于研究平衡态和可逆过程,其主要原因是长期以来整个非平衡态热力学缺乏一个较为令人满意的理论.但在最近二、三十年间非平衡态热力学取得了巨大的进展.本文简要讨论与化学反应有关的非平衡态热力学的进展.     

A Stochastic Extension of Macroscopic Stability Criterion of Nonequilibrium Steady State in Chemical Reaction Systems Governed by Master Equation

By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .     

Fluctuation theorem for nonequilibrium reactions

A fluctuation theorem is derived for stochastic nonequilibrium reactions ruled by the chemical master equation. The theorem is expressed in terms of the generating and large-deviation functions characterizing the fluctuations of a quantity which measures the loss of detailed balance out of thermodynamic equilibrium. The relationship to entropy production is established and discussed. The fluctuation theorem is verified in the Schl?gl model of far-from-equilibrium bistability.     

Potential and flux decomposition for dynamical systems and non-equilibrium thermodynamics: curvature, gauge field, and generalized fluctuation-dissipation theorem

The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance. The response due to a small perturbation can be expressed by a spontaneous fluctuation. For non-equilibrium systems, we derived a generalized FDT that the response function is composed of two parts: (1) a spontaneous correlation representing the relaxation which is present in the near equilibrium systems with detailed balance and (2) a correlation related to the persistence of the curl flux in steady state, which is also in part linked to a internal curvature of a gauge field. The generalized FDT is also related to the fluctuation theorem. In the equal time limit, the generalized FDT naturally leads to non-equilibrium thermodynamics where the entropy production rate can be decomposed into spontaneous relaxation driven by gradient force and house keeping contribution driven by the non-zero flux that sustains the non-equilibrium environment and breaks the detailed balance. On any particular path, the medium heat dissipation due to the non-zero curl flux is analogous to the Wilson lines of an Abelian gauge theory.     

Entropy production as a universal functional of reaction rate: chemical networks close to steady states

Entropy production rate (EPR) is the fundamental theoretical quantity in non-equilibrium thermodynamics whereas reaction rate is the primary experimental quantity for a chemical system out-of-equilibrium. In this work, we explore a connection between the above two quantities for general reaction networks. Both cyclic and linear networks of arbitrary dimension are studied, along with a mixed variety. The systems can attain a non-equilibrium steady state (NESS) under chemiostatic condition, which becomes the state of true thermodynamic equilibrium when detailed balance holds. We show that there exists a universal functional relationship of the EPR with reaction rate close to steady states for all the networks considered. Near a NESS, the former varies linearly with the reaction rate. On the other hand, around a true equilibrium, it varies quadratically with the latter. Numerical experiments justify our analytical findings quite transparently.     

Entropic estimate of cooperative binding of substrate on a single oligomeric enzyme: an index of cooperativity

Here we have systematically studied the cooperative binding of substrate molecules on the active sites of a single oligomeric enzyme in a chemiostatic condition. The average number of bound substrate and the net velocity of the enzyme catalyzed reaction are studied by the formulation of stochastic master equation for the cooperative binding classified here as spatial and temporal. We have estimated the entropy production for the cooperative binding schemes based on single trajectory analysis using a kinetic Monte Carlo technique. It is found that the total as well as the medium entropy production shows the same generic diagnostic signature for detecting the cooperativity, usually characterized in terms of the net velocity of the reaction. This feature is also found to be valid for the total entropy production rate at the non-equilibrium steady state. We have introduced an index of cooperativity, C, defined in terms of the ratio of the surprisals or equivalently, the stochastic system entropy associated with the fully bound state of the cooperative and non-cooperative cases. The criteria of cooperativity in terms of C is compared with that of the Hill coefficient of some relevant experimental result and gives a microscopic insight on the mechanism of cooperative binding of substrate on a single oligomeric enzyme which is usually estimated from the macroscopic reaction rate.     

Steady-state fluctuations of a genetic feedback loop: an exact solution

Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence, exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene regulatory feedback loop: a gene produces protein which then binds to the promoter of the same gene and regulates its expression. The protein degrades in its free and bound forms. This network breaks detailed balance and involves a single bimolecular reaction step. We provide an exact solution of the steady-state master equation for arbitrary values of the parameters, and present simplified solutions for a number of special cases. The full parametric dependence of the analytical non-equilibrium steady-state probability distribution is verified by direct numerical solution of the master equations. For the case where the degradation rate of bound and free protein is the same, our solution is at variance with a previous claim of an exact solution [J. E. M. Hornos, D. Schultz, G. C. P. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic, and P. G. Wolynes, Phys. Rev. E 72, 051907 (2005), and subsequent studies]. We show explicitly that this is due to an unphysical formulation of the underlying master equation in those studies.