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第425行：
第425行： + 第430行：
第431行： − 经典平衡态热力学的基本关系+ 第446行：
第447行： − 表示系统熵的变化是密集量，温度，数学，压力，数学，化学势，以及大量能量的微分的函数。+ 第454行：
第455行： − 在昂萨格(1931，i)之后，让我们将我们的考虑扩展到热力学非平衡系统。作为基础，我们需要宏观量的局部定义版本。宏观量的局部定义版本。+ 第462行：
第463行： − 对于经典的非平衡研究，我们将考虑一些新的局部定义的强烈的宏观变量。我们可以在适当的条件下，通过局部定义基本局部定义的宏观量的梯度和通量密度，导出这些新的变量。+ 第470行：
第471行： − 这种局部定义的强烈宏观变量梯度被称为“热力学力”。它们“驱动”通量密度，也许常被误称为“通量” ，这是力的双重作用。这些量在关于昂萨格互反关系的文章中定义。+ 第563行：
第564行： − −
→Flows and forces
==Flows and forces==
==Flows and forces==
流和力
The fundamental relation of classical equilibrium thermodynamics <ref name="W. Greiner et. al. 1997">W. Greiner, L. Neise, and H. Stöcker (1997), ''Thermodynamics and Statistical Mechanics (Classical Theoretical Physics)'' ,Springer-Verlag, New York, '''P85, 91, 101,108,116''', {{ISBN|0-387-94299-8}}.</ref>
The fundamental relation of classical equilibrium thermodynamics <ref name="W. Greiner et. al. 1997">W. Greiner, L. Neise, and H. Stöcker (1997), ''Thermodynamics and Statistical Mechanics (Classical Theoretical Physics)'' ,Springer-Verlag, New York, '''P85, 91, 101,108,116''', {{ISBN|0-387-94299-8}}.</ref>
The fundamental relation of classical equilibrium thermodynamics
The fundamental relation of classical equilibrium thermodynamics
经典平衡态热力学的基本关系为
expresses the change in entropy <math>dS</math> of a system as a function of the intensive quantities temperature <math>T</math>, pressure <math>p</math> and <math>i^{th}</math> chemical potential <math>\mu_i</math> and of the differentials of the extensive quantities energy <math>U</math>, volume <math>V</math> and <math>i^{th}</math> particle number <math>N_i</math>.
expresses the change in entropy <math>dS</math> of a system as a function of the intensive quantities temperature <math>T</math>, pressure <math>p</math> and <math>i^{th}</math> chemical potential <math>\mu_i</math> and of the differentials of the extensive quantities energy <math>U</math>, volume <math>V</math> and <math>i^{th}</math> particle number <math>N_i</math>.
表示系统熵的变化 <math>dS</math> 是强度量温度<math>T</math>、压强<math>p</math>、第i个化学势<math>\mu_i</math>以及广延量能量<math>U</math>、体积<math>V</math>、第i个粒子数目<math>N_i</math>的微分的函数。
Following Onsager (1931,I), let us extend our considerations to thermodynamically non-equilibrium systems. As a basis, we need locally defined versions of the extensive macroscopic quantities <math>U</math>, <math>V</math> and <math>N_i</math> and of the intensive macroscopic quantities <math>T</math>, <math>p</math> and <math>\mu_i</math>.
Following Onsager (1931,I), let us extend our considerations to thermodynamically non-equilibrium systems. As a basis, we need locally defined versions of the extensive macroscopic quantities <math>U</math>, <math>V</math> and <math>N_i</math> and of the intensive macroscopic quantities <math>T</math>, <math>p</math> and <math>\mu_i</math>.
跟随昂萨格(1931，I)，让我们扩展到热力学非平衡系统。作为基础，我们需要定义宏观广延量 <math>U</math>、<math>V</math>、<math>N_i</math>和宏观强度量<math>T</math>, <math>p</math> 、 <math>\mu_i</math>的局部版本。
For classical non-equilibrium studies, we will consider some new locally defined intensive macroscopic variables. We can, under suitable conditions, derive these new variables by locally defining the gradients and flux densities of the basic locally defined macroscopic quantities.
For classical non-equilibrium studies, we will consider some new locally defined intensive macroscopic variables. We can, under suitable conditions, derive these new variables by locally defining the gradients and flux densities of the basic locally defined macroscopic quantities.
对于经典的非平衡研究，我们将考虑一些新定义的局部宏观强度量。我们可以在适当的条件下，通过局部定义基本局部宏观量的梯度和流密度，导出这些新的变量。
Such locally defined gradients of intensive macroscopic variables are called 'thermodynamic forces'. They 'drive' flux densities, perhaps misleadingly often called 'fluxes', which are dual to the forces. These quantities are defined in the article on Onsager reciprocal relations.
Such locally defined gradients of intensive macroscopic variables are called 'thermodynamic forces'. They 'drive' flux densities, perhaps misleadingly often called 'fluxes', which are dual to the forces. These quantities are defined in the article on Onsager reciprocal relations.
这种局部定义的宏观强度量的梯度被称为“热力学力”。它们“驱动”流密度，也许常被误称为“流” ，这是双重的力。这些量在关于昂萨格倒易关系的文章中有定义。
上述方程的熵产生率的推广是由 Pokrovskii 给出的。
上述方程的熵产生率的推广是由 Pokrovskii 给出的。
==Speculated extremal principles for non-equilibrium processes==
==Speculated extremal principles for non-equilibrium processes==