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==Entropy in evolving systems==

==Entropy in evolving systems==

It is pointed out by W.T. Grandy Jr,<ref>{{cite journal | doi = 10.1023/B:FOOP.0000012007.06843.ed | title = Time Evolution in Macroscopic Systems. I. Equations of Motion | year = 2004 | last1 = Grandy | first1 = W.T., Jr. | journal = Foundations of Physics | volume = 34 | issue = 1 | page = 1 |url=http://physics.uwyo.edu/~tgrandy/evolve.html |arxiv = cond-mat/0303290 |bibcode = 2004FoPh...34....1G }}</ref><ref>{{cite journal | url=http://physics.uwyo.edu/~tgrandy/entropy.html | doi=10.1023/B:FOOP.0000012008.36856.c1 | title=Time Evolution in Macroscopic Systems. II. The Entropy | year=2004 | last1=Grandy | first1=W.T., Jr. | journal=Foundations of Physics | volume=34 | issue=1 | page=21 |arxiv = cond-mat/0303291 |bibcode = 2004FoPh...34...21G }}</ref><ref>{{cite journal | url=http://physics.uwyo.edu/~tgrandy/applications.html | doi = 10.1023/B:FOOP.0000022187.45866.81 | title=Time Evolution in Macroscopic Systems. III: Selected Applications | year=2004 | last1=Grandy | first1=W. T., Jr | journal=Foundations of Physics | volume=34 | issue=5 | page=771 |bibcode = 2004FoPh...34..771G }}</ref><ref>Grandy 2004 see also [http://physics.uwyo.edu/~tgrandy/Statistical_Mechanics.html].</ref> 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,<ref>{{cite journal | doi = 10.1023/B:FOOP.0000012007.06843.ed | title = Time Evolution in Macroscopic Systems. I. Equations of Motion | year = 2004 | last1 = Grandy | first1 = W.T., Jr. | journal = Foundations of Physics | volume = 34 | issue = 1 | page = 1 |url=http://physics.uwyo.edu/~tgrandy/evolve.html |arxiv = cond-mat/0303290 |bibcode = 2004FoPh...34....1G }}</ref><ref>{{cite journal | url=http://physics.uwyo.edu/~tgrandy/entropy.html | doi=10.1023/B:FOOP.0000012008.36856.c1 | title=Time Evolution in Macroscopic Systems. II. The Entropy | year=2004 | last1=Grandy | first1=W.T., Jr. | journal=Foundations of Physics | volume=34 | issue=1 | page=21 |arxiv = cond-mat/0303291 |bibcode = 2004FoPh...34...21G }}</ref><ref>{{cite journal | url=http://physics.uwyo.edu/~tgrandy/applications.html | doi = 10.1023/B:FOOP.0000022187.45866.81 | title=Time Evolution in Macroscopic Systems. III: Selected Applications | year=2004 | last1=Grandy | first1=W. T., Jr | journal=Foundations of Physics | volume=34 | issue=5 | page=771 |bibcode = 2004FoPh...34..771G }}</ref><ref>Grandy 2004 see also [http://physics.uwyo.edu/~tgrandy/Statistical_Mechanics.html].</ref> 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.

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。

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。

方程式右边的第一项代表了进入系统的热能流; 最后一项ーー进入系统的能量流，伴随着粒子流进入系统，粒子流可以是正的也可以是负的。第一部分的中期描述了由于内部变量的松弛而引起的能量耗散(产生熵)。在化学反应物质的情况下，由普利戈金研究，内部变量似乎是测量不完全的化学反应，也就是测量多少考虑的体系与化学反应是不平衡的。这个理论可以推广，把任何偏离平衡态的情况看作是一个内变量，因此我们认为方程式(1)中的内变量集合不仅包含了定义系统中所有化学反应完全程度的量，而且还包含了系统的结构、温度梯度、物质浓度差等。

方程式右边的第一项代表了进入系统的热能流; 最后一项ーー进入系统的能量流，伴随着粒子流进入系统，粒子流可以是正的也可以是负的。第一部分的中期描述了由于内部变量的松弛而引起的能量耗散(产生熵)。在化学反应物质的情况下，由普利戈金研究，内部变量似乎是测量不完全的化学反应，也就是测量多少考虑的体系与化学反应是不平衡的。这个理论可以推广，把任何偏离平衡态的情况看作是一个内变量，因此我们认为方程式(1)中的内变量集合不仅包含了定义系统中所有化学反应完全程度的量，而且还包含了系统的结构、温度梯度、物质浓度差等。

==Flows and forces==

==Flows and forces==