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→Entropy in evolving systems
It is pointed out by W.T. Grandy Jr, that entropy, though it may be defined for a non-equilibrium system is—when strictly considered—only a macroscopic quantity that refers to the whole system, and is not a dynamical variable and in general does not act as a local potential that describes local physical forces. Under special circumstances, however, one can metaphorically think as if the thermal variables behaved like local physical forces. The approximation that constitutes classical irreversible thermodynamics is built on this metaphoric thinking.
It is pointed out by W.T. Grandy Jr, that entropy, though it may be defined for a non-equilibrium system is—when strictly considered—only a macroscopic quantity that refers to the whole system, and is not a dynamical variable and in general does not act as a local potential that describes local physical forces. Under special circumstances, however, one can metaphorically think as if the thermal variables behaved like local physical forces. The approximation that constitutes classical irreversible thermodynamics is built on this metaphoric thinking.
W.T. Grandy Jr 指出，熵虽然可以被定义为非平衡系统，但是在严格考虑时，它只是一个指向整个系统的宏观量，而不是一个动力学变量，一般不作为描述局部物理力的局部势。然而，在特殊情况下，人们可以隐喻地认为，热变量表现得像局部物理力量。构成经典不可逆热力学的近似是建立在这种隐喻思维之上的。
W.T. Grandy Jr 指出，熵虽然在非平衡系统中可以定义，但是严格来说，它只是一个关于整个系统的宏观量，而不是一个动力学变量，一般不作为描述局部力的局部势能。然而在特殊情况下，人们可以隐喻地认为，热力学变量表现得像局部物理力。构成经典不可逆热力学的近似是建立在这种隐喻思维之上的。
This point of view shares many points in common with the concept and the use of entropy in continuum thermomechanics, which evolved completely independently of statistical mechanics and maximum-entropy principles.
This point of view shares many points in common with the concept and the use of entropy in continuum thermomechanics, which evolved completely independently of statistical mechanics and maximum-entropy principles.
这种观点与连续热力学中熵的概念和使用有许多共同点，连续热力学的发展完全独立于统计力学和最大熵原理。
===Entropy in non-equilibrium===
===Entropy in non-equilibrium===
非平衡中的熵
To describe deviation of the thermodynamic system from equilibrium, in addition to constitutive variables <math>x_1, x_2, ..., x_n</math> that are used to fix the equilibrium state, as was described above, a set of variables <math>\xi_1, \xi_2,\ldots</math> that are called internal variables have been introduced. The equilibrium state is considered to be stable and the main property of the internal variables, as measures of non-equilibrium of the system, is their trending to disappear; the local law of disappearing can be written as relaxation equation for each internal variable
To describe deviation of the thermodynamic system from equilibrium, in addition to constitutive variables <math>x_1, x_2, ..., x_n</math> that are used to fix the equilibrium state, as was described above, a set of variables <math>\xi_1, \xi_2,\ldots</math> that are called internal variables have been introduced. The equilibrium state is considered to be stable and the main property of the internal variables, as measures of non-equilibrium of the system, is their trending to disappear; the local law of disappearing can be written as relaxation equation for each internal variable
为了描述热力学系统偏离平衡状态，除了用于确定平衡状态的本构变量<math>x_1, x_2, ..., x_n</math> 之外，还引入了一组称为内部变量的变量 <math>\xi_1, \xi_2,\ldots</math> 。平衡态被认为是稳定的，内部变量作为系统非平衡的度量，其主要性质是它们趋于消失，消失的局部规律可以写成每个内变部量的弛豫方程
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where <math> \tau_i= \tau_i(T, x_1, x_2, \ldots, x_n)</math> is a relaxation time of a corresponding variables. It is convenient to consider the initial value <math> \xi_i^0</math> are equal to zero. The above equation is valid for small deviations from equilibrium; The dynamics of internal variables in general case is considered by Pokrovskii.
where <math> \tau_i= \tau_i(T, x_1, x_2, \ldots, x_n)</math> is a relaxation time of a corresponding variables. It is convenient to consider the initial value <math> \xi_i^0</math> are equal to zero. The above equation is valid for small deviations from equilibrium; The dynamics of internal variables in general case is considered by Pokrovskii.
其中 < math > tau _ i = tau _ i (t，x _ 1，x _ 2，ldots，x _ n) </math > 是对应变量的松弛时间。考虑初始值 < math > xi _ i ^ 0 </math > 等于零是很方便的。上述方程适用于小偏离均衡的情况，Pokrovskii 考虑了一般情况下内变量的动力学。
其中 <math> \tau_i= \tau_i(T, x_1, x_2, \ldots, x_n)</math> 是相应变量的弛豫时间。考虑初始值 <math> \xi_i^0</math> 等于零是方便的。上述方程适用于偏离平衡较小的情况，Pokrovskii 考虑了一般情况下内部变量的动力学。
Entropy of the system in non-equilibrium is a function of the total set of variables
Entropy of the system in non-equilibrium is a function of the total set of variables
非平衡态系统的熵是所有变量集合的函数
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The essential contribution to the thermodynamics of the non-equilibrium systems was brought by Prigogine, when he and his collaborators investigated the systems of chemically reacting substances. The stationary states of such systems exists due to exchange both particles and energy with the environment. In section 8 of the third chapter of his book, Prigogine has specified three contributions to the variation of entropy of the considered system at the given volume and constant temperature <math> T</math> . The increment of entropy <math> S</math> can be calculated according to the formula
The essential contribution to the thermodynamics of the non-equilibrium systems was brought by Prigogine, when he and his collaborators investigated the systems of chemically reacting substances. The stationary states of such systems exists due to exchange both particles and energy with the environment. In section 8 of the third chapter of his book, Prigogine has specified three contributions to the variation of entropy of the considered system at the given volume and constant temperature <math> T</math> . The increment of entropy <math> S</math> can be calculated according to the formula
对非平衡系统热力学的最重要贡献是由普利高津给出的，当时他和他的合作者研究了化学反应物质系统。由于粒子和能量与环境的交换，这类系统的静止状态是存在的。在他的书的第三章的第8节中，普里高金详细说明了在给定的体积和恒定的温度下，被考虑系统的熵的变化有三个贡献。根据该公式可以计算出熵的增量 s </math >
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