强迫耗散系统的有序结构和系统的发展(Ⅰ)，最小熵产生原理和有序结构

一个系统的发展总是由不可逆热力过程和非线性动力过程所驱动.将大气动力学方程组同考虑了动能变化的Gibbs关系结合起来构建的熵平衡方程，才能更好地描述大气系统的不可逆热力过程和非线性动力过程.至今非平衡态热力学仅利用Onsager线性唯象关系证明了最小熵产生原理.利用新建立的熵平衡方程和大气动力学方程的性质证明，最小熵产生原理在热力学线性区和非线性区都是普遍成立的.且当热量输送平衡、水汽输送平衡和动量输送平衡时，系统达到不可逆过程最弱的最小熵产生热力学状态.当系统又是动力平衡且无平流时，这种最小熵产生态就是 关键词： 非线性热力学 熵产生 最小熵产生原理 有序结构     

Entropy production and its positivity in nonlinear response theory of quantum dynamical systems

A formulation ofentropy production is given with the aid of relative entropy in the nonlinear response theory of a quantum dynamical system. It allows a natural interpretation of the quantity in terms of familiar thermodynamic notions, such as force and response current conjugate to it, without sacrificing the full nonlinearity in the perturbing force. For the understanding ofdissipativity aspositive entropy production, the stationarity of states and coarse graining of time scale turn out to be essential, which are implemented by some time averaging procedures involvingalmost periodic external forces. Finally, it is shown that the obtained result reduces, in the linear response regime, to the power dissipation appearing in the well-known fluctuation-dissipation relation.     

非平衡热力学中传热过程熵产表达式的修正

熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.     

On the production of entropy within the concept of incomplete description of states

We calculate the linear response production of relevant entropy as defined recently by Balian. This quantity is — in contrast to the production of entropy defined in thermodynamics of irreversible processes — not determined by the linear transport coefficients alone but depends also on the susceptibilities with respect to the relevant observables. However, for systems satisfying a generalized ergodicity criterion the two expressions for the entropy production coincide.     

On the entropy production for the Davies model of heat conduction

The formula for the entropy production in open quantum systems is examined for the Davies model of heat conduction.This work is supported by Polish Ministry of Higher Education Science and Technology, project MRI 7.     

Deviations from minimum entropy production at steady states of reacting chemical systems arbitrarily close to equilibrium

Our analysis of reacting systems displaced from equilibrium by a matter flux across the boundaries has shown that the state of minimum entropy production differs from the steady state, even in the near equilibrium regime. When the displacement δ from equilibrium is small, the derivative of the dissipation at the steady state and the dissipation itself are both of order δ². The state of least dissipation is displaced from the steady state by terms of order δ² in the species concentrations. The theorem of minimum entropy production may be derived by first truncating the series expansions for the reaction rates, affinities and dissipation assuming that δ is small, and then differentiating to locate the minimum of the dissipation within the resulting idealized model. For chemical systems with an arbitrarily small but macroscopic displacement from equilibrium, this truncation procedure establishes that the dissipation is comparatively small in a neighborhood of the steady state; but it causes large relative errors in the values of the concentration derivatives and time derivatives of the dissipation within that neighborhood, because the operations of series truncation and differentiation do not commute near the steady state, when δ is small but nonzero. Near the steady state, the concentration derivative of the term of order δ³ in the dissipation is comparable to or larger than the derivative of the δ² term.     

Minimum entropy production and logarithmic rate equations

A system interacting with a heat bath and radiation is considered. It is assumed that the steady state is exactly characterized by the principle of minimum entropy production. From this, the general form of the equations for the time rate of change of the probabilities of the states is derived and the rate equations are shown to be nonlinear and to involve the differences of the logarithms of the probabilities. Some properties of these equations are discussed and the specific cases of two- and three-state subsystems are considered and compared with results obtained from the usual linear rate equations.     

On entropy production

We investigate the case of a dynamical system when irreversible time evolution is generated by a nonHermitian superoperator on the states of the system. We introduce a generalized scalar product which can be used to construct a monotonically changing functional of the state, a generalized entropy. This will depend on the level of system dynamics described by the evolution equation. In this paper we consider the special case when the irreversibility derives from imbedding the system of interest into a thermal reservoir. The ensuing time evolution is shown to be compatible both with equilibrium thermodynamics and the entropy production near the final steady state. In particular, Prigogine’s principle of minimum entropy production is discussed. Also the limit of zero temperature is considered. We present comments on earlier treatments.     

Generalized entropy production analysis for mechanism reduction

The paper introduces a generalized formulation for the computation of the relative contribution of each elementary reaction to the total entropy production, which has been proposed as a measure of the importance of elementary reactions and used for the reduction of detailed chemical reaction mechanisms. The reduction method is extended for the cases where the principle of detailed balance does not hold or apply, namely in the case of irreversible reactions or when the reverse rate constants are not computed via the thermodynamic equilibrium constants. Using a mechanism for n-butane consisting exclusively of reversible reactions, the new formulation is compared to the original one, and then applied for the construction of a skeletal mechanism for n-dodecane starting from a detailed mechanism which includes predominantly irreversible reactions. The skeletal scheme is found to accurately capture the ignition delay times over an extended range of pressure, initial temperature and equivalence ratio, the steady-state temperature as function of the residence time in a non-isothermal adiabatic perfectly stirred reactor, and the laminar flame speed of atmospheric flames at different unburned mixture temperatures and equivalence ratios.     

热波传递过程中的熵产分析

傅里叶导热定律导出的温度演化方程将得出无限大的热扰动传播速率。为了克服这个问题,一些修正导热模型被提出,可以得到双曲型温度方程,保证有限的热波传播速率。但是,新的传热模型得出的温度演化将使现有的不可逆热力学中熵产不能保持正定。拓展不可逆热力学通过修正熵以及熵产的表达式,使双曲导热也能得到正定的熵产率。热质理论用力学的概...     

Entropy production and thermal conductivity of a dilute gas

It is known that the thermal conductivity of a dilute gas can be derived by using kinetic theory. We present here a new derivation by starting with two known entropy production principles: the steepest entropy ascent (SEA) principle and the maximum entropy production (MEP) principle. A remarkable feature of the new derivation is that it does not require the specification of the existence of the temperature gradient. The known result is reproduced in a similar form.     

(火积)耗散理论在换热器设计中的应用

本文首先说明(火积)耗散理论避免了最小熵产原理和傅里叶定律间的矛盾,显示了其在处理导热问题上的优越性.然后利用热力学(火积)和熵的关系,推出了换热器中由流体阻力引起的(火积)耗散表达式.     

强迫耗散系统的有序结构和系统的发展(Ⅱ)，广义能量极小值原理和系统的发展

利用大气非线性动力学证明了广义能量极小值原理，进一步从理论上证明它是同大气非平衡 态热力学最小熵产生原理在物理上是一致的.前者表明，强迫耗散动力系统的终态广义能量 达极小值；而最小熵产生原理表明，远离热力学平衡态的开放系其终态时系统内部的不可逆 过程最弱.而且，系统广义能量达极小值和系统熵产生达极小值的终态一般是一个稳定的定 态，它对应着系统的某种有序结构.也就是说它是一个“低耗高效”的有序定态.大气系统作 为自然界一个典型的物理复杂系统，其最小熵产生原理和广义能量极小值原理隐示了自然界 复杂系统的一个一 关键词： 强迫耗散系统 能量极值原理 有序结构 动力系统     

熵产生率公式及其应用

导出了6N维和6维相空间的熵产生率，即熵增加定律的一个统计公式：P=kD(Δ_{qθ)²，即熵产生率P等于扩散系数D、离开平衡率θ的空间梯度平方的平均值与Boltzm ann常数k 三者之乘积.指明非平衡系统的宏观熵产生是由其微观状态数密度在空间随机地不均匀离开 平衡引起的.作为公式的应用,研究了气体自由膨胀、布朗运动及固体变形和断裂三个非平衡 态课题，给出了它们的熵产生及其一次和二次时间变化率，得到了不可逆过程的系统内对应 的微观结构变化是不均匀的推论.进而导 关键词： 熵产生率 微观状态数密度 离开平衡率 随机扩散}     

Stationary open systems: A brief review on contemporary theories on irreversibility

Open systems are very important in science and engineering for their applications and the analysis of the real word. At their steady state, two apparently opposed principles for their rate of entropy production have been proposed: the minimum entropy production rate and the maximum entropy production, useful in the analysis of dissipation and irreversibility of different processes in physics, chemistry, biology and engineering. Both principles involve an extremum of the rate of the entropy production at the steady state under non-equilibrium conditions. On the other hand, in engineering thermodynamics, dissipation and irreversibility are analyzed using the entropy generation, for which there exist two principle of extrema too, the minimum and the maximum principle. Finally, oppositions to the extrema principle have been developed too. In this paper, all these extrema principles will be analyzed in order to point out the relations among them and a synthesis useful in engineering applications, in physical and chemical process analysis and in biology and biotechnology will be proposed.     

Fluctuation theorem and thermodynamic entropy

The validity of the identification of a dissipation function appearing in the recently proved fluctuation theorem to the thermodynamic entropy production has been studied for a classical nonlinear Schlögl reaction. This example has indicated that such identification is unjustified. Owing to this result, the applied importance of the mentioned theorem for studying complex nonequilibrium systems is doubtful.     

热传导的最小熵产生原理

指出某文献对热传导中的最小熵产生的误解，阐明热传导中最小熵产生原理的意义。     

不同目的热优化目标函数:热量传递势容损耗与熵产

热量传递势容(势容)反映了物体的导热能力,在导热过程中势容有损耗,对应于势容损耗最小的导热过程效率最高,传热速率最大。熵反映了过程的不可逆性,在导热过程中熵有增加(熵产),对应于熵产最小的过程是系统做有用功的能力((?))损失最小的过程。以势容损耗和熵产为目标函数,分别对导热平板和圆形导热管进行了导热优化计算。以势容损耗作为目标函数的优化,要求沿传热方向温度的梯度为常数,结果是系统具有最大的导热能力。以熵产作为目标函数的优化,要求沿传热方向温度的自然对数的梯度为常数,结果是系统具有最小的(?)损耗。