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第194行：
第194行： − + − − The scope of present-day non-equilibrium thermodynamics does not cover all physical processes. A condition for the validity of many studies in non-equilibrium thermodynamics of matter is that they deal with what is known as local thermodynamic equilibrium. − − 当今非平衡态热力学的范围并不包括所有的物理过程。在物质的非平衡态热力学几年，许多研究有效的一个条件是，他们处理的是所谓的局部热力学平衡。 − − + − Local thermodynamic equilibrium of matter The longer relaxation time is of the order of magnitude of times taken for the macroscopic dynamical structure of the system to change. The shorter is of the order of magnitude of times taken for a single 'cell' to reach local thermodynamic equilibrium. If these two relaxation times are not well separated, then the classical non-equilibrium thermodynamical concept of local thermodynamic equilibrium loses its meaning He defined 'local thermodynamic equilibrium' in a 'cell' by requiring that it macroscopically absorb and spontaneously emit radiation as if it were in radiative equilibrium in a cavity at the temperature of the matter of the 'cell'. Then it strictly obeys Kirchhoff's law of equality of radiative emissivity and absorptivity, with a black body source function. The key to local thermodynamic equilibrium here is that the rate of collisions of ponderable matter particles such as molecules should far exceed the rates of creation and annihilation of photons. − 物质的局部热力学平衡较长的弛豫时间是系统宏观动力学结构发生变化所需时间的数量级。较短的一个数量级是一个单细胞到达本地热力学平衡所需的时间。如果这两个弛豫时间没有很好地分开，那么局部热力学平衡的经典的非平衡热力学概念就失去了它的意义。他定义了“细胞中的局部热力学平衡” ，要求它在宏观上吸收和自发地发射辐射，就好像它在一个与“细胞”物质温度相当的辐射平衡中一样。然后严格遵守基尔霍夫辐射发射率和吸收率相等的定律，使用一个黑体源函数。这里局域热力学平衡的关键在于，可重物质粒子的碰撞速率，比如分子，应该远远超过光子的产生和湮灭速率。+ − If the stationary state of the process is stable, then the unreproducible fluctuations involve local transient decreases of entropy. The reproducible response of the system is then to increase the entropy back to its maximum by irreversible processes: the fluctuation cannot be reproduced with a significant level of probability. Fluctuations about stable stationary states are extremely small except near critical points (Kondepudi and Prigogine 1998, page 323).<ref>Kondepudi, D., Prigogine, I, (1998). ''Modern Thermodynamics. From Heat Engines to Dissipative Structures'', Wiley, Chichester, 1998, {{ISBN|0-471-97394-7}}.</ref> The stable stationary state has a local maximum of entropy and is locally the most reproducible state of the system. There are theorems about the irreversible dissipation of fluctuations. Here 'local' means local with respect to the abstract space of thermodynamic coordinates of state of the system.+ 第216行：
第210行： − 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.+ − − 这是 w.t. 指出的。Grandy Jr 认为，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。 − −
→Stationary states, fluctuations, and stability
可以证明，不管是否建立在平衡状态下，勒让德变换都在扩展的马休函数的最小状态下改变熵（在平衡时有效）的最大状态。
可以证明，不管是否建立在平衡状态下，勒让德变换都在扩展的马休函数的最小状态下改变熵（在平衡时有效）的最大状态。
==Stationary states, fluctuations, and stability==
== Stationary states, fluctuations, and stability 平稳状态，波动性和稳定性==
In thermodynamics one is often interested in a stationary state of a process, allowing that the stationary state include the occurrence of unpredictable and experimentally unreproducible fluctuations in the state of the system. The fluctuations are due to the system's internal sub-processes and to exchange of matter or energy with the system's surroundings that create the constraints that define the process.
In thermodynamics one is often interested in a stationary state of a process, allowing that the stationary state include the occurrence of unpredictable and experimentally unreproducible fluctuations in the state of the system. The fluctuations are due to the system's internal sub-processes and to exchange of matter or energy with the system's surroundings that create the constraints that define the process.
在热力学中，人们通常对过程的静态感兴趣，因为它涵盖了系统状态下发生的不可预测的和实验上不可再现的波动。波动是由于系统内部的子过程以及与系统周围的物质或能量交换引起的，从而形成了定义过程的约束。
If the stationary state of the process is stable, then the unreproducible fluctuations involve local transient decreases of entropy. The reproducible response of the system is then to increase the entropy back to its maximum by irreversible processes: the fluctuation cannot be reproduced with a significant level of probability. Fluctuations about stable stationary states are extremely small except near critical points (Kondepudi and Prigogine 1998, page 323). <ref>Kondepudi, D., Prigogine, I, (1998). ''Modern Thermodynamics. From Heat Engines to Dissipative Structures'', Wiley, Chichester, 1998, {{ISBN|0-471-97394-7}}. </ref> The stable stationary state has a local maximum of entropy and is locally the most reproducible state of the system. There are theorems about the irreversible dissipation of fluctuations. Here 'local' means local with respect to the abstract space of thermodynamic coordinates of state of the system.
如果静态反应过程是稳定的，则不可重现的波动会涉及到熵的局部瞬时减小过程。系统的可重现响应是通过不可逆过程将熵增加回最大值：即不能以很大的概率再现波动。除了接近临界点外，关于稳态的波动很小（Kondepudi和Prigogine 1998，第323页）。稳定的静止状态具有局部的熵最大值，并且该系统最可能出现局部性重现响应状态。关于波动的不可逆耗散存在一些与之相关的定理。这里的“局部”是指相对于系统状态下热力学坐标的抽象空间而言的。
If the stationary state is unstable, then any fluctuation will almost surely trigger the virtually explosive departure of the system from the unstable stationary state. This can be accompanied by increased export of entropy.
If the stationary state is unstable, then any fluctuation will almost surely trigger the virtually explosive departure of the system from the unstable stationary state. This can be accompanied by increased export of entropy.
如果静态反应过程是不稳定的，那么任何波动都很大概率会触发系统从不稳定的静止状态下产生爆炸，并伴随着熵输出的增加。
==Local thermodynamic equilibrium==
==Local thermodynamic equilibrium==