更改

==Scope==

==Scope 范围==

 

定义非平衡热力学状态变量的合适关系如下所述。当系统处于足够接近热力学平衡态的状态时，非平衡态变量可以通过与测量热力学状态变量相同的技术，足够精确地在局部测量,或者通过相应的时间和空间导数得到，包括物质和能量的流。一般来说，非平衡态热力学系统在空间和时间上都是不均匀的，但是它们的不均匀性仍然具有足够的光滑度，使得非平衡态变量存在合适的时间和空间导数。由于空间的非均匀性，非平衡态对应的热力学广延量必须定义为平衡态中相应广延量的空间密度。在系统足够接近热力学平衡的情况下，非平衡态的强度量，例如温度和压强，与平衡状态变量密切对应。为了刻画相应的非均匀性，测量探头必须足够小，响应速度也必须足够快。此外，非平衡状态变量之间需要在数学上和功能上相互关联，以适当的类似于平衡热力学状态变量之间对应关系的方式。在现实中这些要求是非常苛刻的，并且可能很难，或者说在实际上，甚至在理论上都不可能满足。这就一部分解释了为什么非平衡态热力学是一个仍在进展中的工作。

定义非平衡热力学状态变量的合适关系如下所述。当系统处于足够接近热力学平衡态的状态时，非平衡态变量可以通过与测量热力学状态变量相同的技术，足够精确地在局部测量,或者通过相应的时间和空间导数得到，包括物质和能量的流。一般来说，非平衡态热力学系统在空间和时间上都是不均匀的，但是它们的不均匀性仍然具有足够的光滑度，使得非平衡态变量存在合适的时间和空间导数。由于空间的非均匀性，非平衡态对应的热力学广延量必须定义为平衡态中相应广延量的空间密度。在系统足够接近热力学平衡的情况下，非平衡态的强度量，例如温度和压强，与平衡状态变量密切对应。为了刻画相应的非均匀性，测量探头必须足够小，响应速度也必须足够快。此外，非平衡状态变量之间需要在数学上和功能上相互关联，以适当的类似于平衡热力学状态变量之间对应关系的方式。在现实中这些要求是非常苛刻的，并且可能很难，或者说在实际上，甚至在理论上都不可能满足。这就一部分解释了为什么非平衡态热力学是一个仍在进展中的工作。

==Overview==

==Overview 概述==

 

Non-equilibrium thermodynamics is a work in progress, not an established edifice. This article is an attempt to sketch some approaches to it and some concepts important for it.

Non-equilibrium thermodynamics is a work in progress, not an established edifice. This article is an attempt to sketch some approaches to it and some concepts important for it.

它的形式非常适合于描述高频过程和小尺度材料。

它的形式非常适合于描述高频过程和小尺度材料。

==Basic concepts==

==Basic concepts 基本概念==

 

There are many examples of stationary non-equilibrium systems, some very simple, like a system confined between two thermostats at different temperatures or the ordinary [[Couette flow]], a fluid enclosed between two flat walls moving in opposite directions and defining non-equilibrium conditions at the walls. [[Laser]] action is also a non-equilibrium process, but it depends on departure from local thermodynamic equilibrium and is thus beyond the scope of classical irreversible thermodynamics; here a strong temperature difference is maintained between two molecular degrees of freedom (with molecular laser, vibrational and rotational molecular motion), the requirement for two component 'temperatures' in the one small region of space, precluding local thermodynamic equilibrium, which demands that only one temperature be needed. Damping of acoustic perturbations or shock waves are non-stationary non-equilibrium processes. Driven [[complex fluids]], turbulent systems and glasses are other examples of non-equilibrium systems.

There are many examples of stationary non-equilibrium systems, some very simple, like a system confined between two thermostats at different temperatures or the ordinary [[Couette flow]], a fluid enclosed between two flat walls moving in opposite directions and defining non-equilibrium conditions at the walls. [[Laser]] action is also a non-equilibrium process, but it depends on departure from local thermodynamic equilibrium and is thus beyond the scope of classical irreversible thermodynamics; here a strong temperature difference is maintained between two molecular degrees of freedom (with molecular laser, vibrational and rotational molecular motion), the requirement for two component 'temperatures' in the one small region of space, precluding local thermodynamic equilibrium, which demands that only one temperature be needed. Damping of acoustic perturbations or shock waves are non-stationary non-equilibrium processes. Driven [[complex fluids]], turbulent systems and glasses are other examples of non-equilibrium systems.

考虑到恒星，爱德华·亚瑟·米尔恩根据每个小局部“单元”中物质的热辐射，给出了局部热力学平衡的定义。他定义一个“单元”中的局部热力学平衡，要求它在宏观上吸收和自发放射辐射时，就好像它处于该“单元”中物质温度的辐射平衡中一样。然后使用一个黑体源函数，严格遵守基尔霍夫辐射发射率和吸收率相等的定律。这里局部热力学平衡的关键在于，像分子这样的有重量物质粒子的碰撞速率，应该远远超过光子的产生和湮灭速率。

考虑到恒星，爱德华·亚瑟·米尔恩根据每个小局部“单元”中物质的热辐射，给出了局部热力学平衡的定义。他定义一个“单元”中的局部热力学平衡，要求它在宏观上吸收和自发放射辐射时，就好像它处于该“单元”中物质温度的辐射平衡中一样。然后使用一个黑体源函数，严格遵守基尔霍夫辐射发射率和吸收率相等的定律。这里局部热力学平衡的关键在于，像分子这样的有重量物质粒子的碰撞速率，应该远远超过光子的产生和湮灭速率。

==Entropy in evolving systems==

==Entropy in evolving systems 演化系统的熵==

 

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.

方程式右边的第一项代表进入系统的热能; 最后一项为伴随着粒子进入系统而带来的能量流，粒子流<math> \Delta N_\alpha </math>可以是正的也可以是负的，<math> \mu_\alpha</math> 是物质<math> \alpha</math>的化学势。方程右边中间项描述了由于内部变量<math> \xi_j</math>的弛豫而引起的能量耗散(熵产生)。在普利高津研究的化学反应物质的情况下，内部变量看起来是测量化学反应的未完成度，也就是测量考虑的化学反应体系远离平衡的程度。这个理论可以推广，把任何对平衡态的偏离看作是内部变量，因此我们认为方程式(1)中的内部变量集合<math> \xi_j</math>不仅包含了定义系统中所有化学反应完成程度的量，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进入系统的热能; 最后一项为伴随着粒子进入系统而带来的能量流，粒子流<math> \Delta N_\alpha </math>可以是正的也可以是负的，<math> \mu_\alpha</math> 是物质<math> \alpha</math>的化学势。方程右边中间项描述了由于内部变量<math> \xi_j</math>的弛豫而引起的能量耗散(熵产生)。在普利高津研究的化学反应物质的情况下，内部变量看起来是测量化学反应的未完成度，也就是测量考虑的化学反应体系远离平衡的程度。这个理论可以推广，把任何对平衡态的偏离看作是内部变量，因此我们认为方程式(1)中的内部变量集合<math> \xi_j</math>不仅包含了定义系统中所有化学反应完成程度的量，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 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>

最近的一项提议或许可以绕过这些阴云密布的前景。

最近的一项提议或许可以绕过这些阴云密布的前景。

==Applications==

==Applications 应用==

 

Non-equilibrium thermodynamics has been successfully applied to describe biological processes such as [[protein folding]]/unfolding and [[membrane transport|transport through membranes]].<ref>{{cite journal |last1=Kimizuka |first1=Hideo |last2=Kaibara |first2=Kozue |title=Nonequilibrium thermodynamics of ion transport through membranes |journal=Journal of Colloid and Interface Science |date=September 1975 |volume=52 |issue=3 |pages=516–525 |doi=10.1016/0021-9797(75)90276-3}}</ref><ref>{{cite journal |last1=Baranowski |first1=B. |title=Non-equilibrium thermodynamics as applied to membrane transport |journal=Journal of Membrane Science |date=April 1991 |volume=57 |issue=2–3 |pages=119–159 |doi=10.1016/S0376-7388(00)80675-4}}</ref>

Non-equilibrium thermodynamics has been successfully applied to describe biological processes such as [[protein folding]]/unfolding and [[membrane transport|transport through membranes]].<ref>{{cite journal |last1=Kimizuka |first1=Hideo |last2=Kaibara |first2=Kozue |title=Nonequilibrium thermodynamics of ion transport through membranes |journal=Journal of Colloid and Interface Science |date=September 1975 |volume=52 |issue=3 |pages=516–525 |doi=10.1016/0021-9797(75)90276-3}}</ref><ref>{{cite journal |last1=Baranowski |first1=B. |title=Non-equilibrium thermodynamics as applied to membrane transport |journal=Journal of Membrane Science |date=April 1991 |volume=57 |issue=2–3 |pages=119–159 |doi=10.1016/S0376-7388(00)80675-4}}</ref>

<ref>{{Cite book|title = The Unity of Science and Economics: A New Foundation of Economic Theory|last = Chen|first = Jing|publisher = Springer|year = 2015|isbn = |location = https://www.springer.com/us/book/9781493934645|pages = }}</ref>

<ref>{{Cite book|title = The Unity of Science and Economics: A New Foundation of Economic Theory|last = Chen|first = Jing|publisher = Springer|year = 2015|isbn = |location = https://www.springer.com/us/book/9781493934645|pages = }}</ref>

==See also==

==See also 其他相关==