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Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of variables (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. It relies on what may be thought of as more or less nearness to thermodynamic equilibrium.  

Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of variables (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. It relies on what may be thought of as more or less nearness to thermodynamic equilibrium.  

非平衡态热力学是热力学的一个分支，研究某些不处于热力学平衡中的物理系统。但是这些系统可以用一些变量(非平衡态变量)来描述，这些变量来源于用来描述热力学平衡系统的变量的外推。非平衡态热力学与输运过程和化学反应速率相关。它依赖于被认为是或多或少接近热力学平衡的东西。

'''非平衡态热力学Non-equilibrium thermodynamics'''是热力学的一个分支，研究某些不处于热力学平衡中的物理系统。但是这些系统可以用一些变量(非平衡态变量)来描述，这些变量来源于用来描述热力学平衡系统的变量的外推。非平衡态热力学与输运过程和化学反应速率相关。它依赖于被认为是或多或少接近热力学平衡的东西。

Equilibrium thermodynamics restricts its considerations to processes that have initial and final states of thermodynamic equilibrium; the time-courses of processes are deliberately ignored. Consequently, equilibrium thermodynamics allows processes that pass through states far from thermodynamic equilibrium, that cannot be described even by the variables admitted for non-equilibrium thermodynamics, such as time rates of change of temperature and pressure. For example, in equilibrium thermodynamics, a process is allowed to include even a violent explosion that cannot be described by non-equilibrium thermodynamics. Equilibrium thermodynamics does, however, for theoretical development, use the idealized concept of the "quasi-static process". A quasi-static process is a conceptual (timeless and physically impossible) smooth mathematical passage along a continuous path of states of thermodynamic equilibrium. It is an exercise in differential geometry rather than a process that could occur in actuality.

Equilibrium thermodynamics restricts its considerations to processes that have initial and final states of thermodynamic equilibrium; the time-courses of processes are deliberately ignored. Consequently, equilibrium thermodynamics allows processes that pass through states far from thermodynamic equilibrium, that cannot be described even by the variables admitted for non-equilibrium thermodynamics, such as time rates of change of temperature and pressure. For example, in equilibrium thermodynamics, a process is allowed to include even a violent explosion that cannot be described by non-equilibrium thermodynamics. Equilibrium thermodynamics does, however, for theoretical development, use the idealized concept of the "quasi-static process". A quasi-static process is a conceptual (timeless and physically impossible) smooth mathematical passage along a continuous path of states of thermodynamic equilibrium. It is an exercise in differential geometry rather than a process that could occur in actuality.

平衡态热力学把它的研究范围局限于具有热力学平衡的初态和末态的过程，过程的时间进程被有意地忽略。因此，平衡态热力学允许物理过程经历过远离热力学平衡的状态，这些状态甚至不能用非平衡态热力学所允许的变量来描述，比如温度和压力的时间变化率。例如在平衡态热力学中，一个过程甚至可以包括一个非平衡态热力学无法描述的剧烈爆炸。然而，为了理论发展，平衡态热力学使用了“准静态过程”的理想化概念。准静态过程是一种概念上(永恒的、物理上不可能的)沿着热力学平衡状态连续路径的平滑数学过程。它是微分几何的练习，而不是现实中可能发生的过程。

平衡态热力学把它的研究范围局限于具有热力学平衡的初态和末态的过程，过程的时间进程被有意地忽略。因此，平衡态热力学允许物理过程经历过远离热力学平衡的状态，这些状态甚至不能用非平衡态热力学所允许的变量来描述，比如温度和压强的时间变化率。例如在平衡态热力学中，一个过程甚至可以包括一个非平衡态热力学无法描述的剧烈爆炸。然而，为了理论发展，平衡态热力学使用了“准静态过程”的理想化概念。准静态过程是一种概念上(永恒的、物理上不可能的)沿着热力学平衡状态连续路径的平滑数学过程。它是微分几何的练习，而不是现实中可能发生的过程。

Non-equilibrium thermodynamics, on the other hand, attempting to describe continuous time-courses, needs its state variables to have a very close connection with those of equilibrium thermodynamics. This profoundly restricts the scope of non-equilibrium thermodynamics, and places heavy demands on its conceptual framework.

Non-equilibrium thermodynamics, on the other hand, attempting to describe continuous time-courses, needs its state variables to have a very close connection with those of equilibrium thermodynamics. This profoundly restricts the scope of non-equilibrium thermodynamics, and places heavy demands on its conceptual framework.

===Non-equilibrium state variables===

===Non-equilibrium state variables===

The suitable relationship that defines non-equilibrium thermodynamic state variables is as follows. On occasions when the system happens to be in states that are sufficiently close to thermodynamic equilibrium, non-equilibrium state variables are such that they can be measured locally with sufficient accuracy by the same techniques as are used to measure thermodynamic state variables, or by corresponding time and space derivatives, including fluxes of matter and energy. In general, non-equilibrium thermodynamic systems are spatially and temporally non-uniform, but their non-uniformity still has a sufficient degree of smoothness to support the existence of suitable time and space derivatives of non-equilibrium state variables. Because of the spatial non-uniformity, non-equilibrium state variables that correspond to extensive thermodynamic state variables have to be defined as spatial densities of the corresponding extensive equilibrium state variables. On occasions when the system is sufficiently close to thermodynamic equilibrium, intensive non-equilibrium state variables, for example temperature and pressure, correspond closely with equilibrium state variables. It is necessary that measuring probes be small enough, and rapidly enough responding, to capture relevant non-uniformity. Further, the non-equilibrium state variables are required to be mathematically functionally related to one another in ways that suitably resemble corresponding relations between equilibrium thermodynamic state variables. In reality, these requirements are very demanding, and it may be difficult or practically, or even theoretically, impossible to satisfy them. This is part of why non-equilibrium thermodynamics is a work in progress.

The suitable relationship that defines non-equilibrium thermodynamic state variables is as follows. On occasions when the system happens to be in states that are sufficiently close to thermodynamic equilibrium, non-equilibrium state variables are such that they can be measured locally with sufficient accuracy by the same techniques as are used to measure thermodynamic state variables, or by corresponding time and space derivatives, including fluxes of matter and energy. In general, non-equilibrium thermodynamic systems are spatially and temporally non-uniform, but their non-uniformity still has a sufficient degree of smoothness to support the existence of suitable time and space derivatives of non-equilibrium state variables. Because of the spatial non-uniformity, non-equilibrium state variables that correspond to extensive thermodynamic state variables have to be defined as spatial densities of the corresponding extensive equilibrium state variables. On occasions when the system is sufficiently close to thermodynamic equilibrium, intensive non-equilibrium state variables, for example temperature and pressure, correspond closely with equilibrium state variables. It is necessary that measuring probes be small enough, and rapidly enough responding, to capture relevant non-uniformity. Further, the non-equilibrium state variables are required to be mathematically functionally related to one another in ways that suitably resemble corresponding relations between equilibrium thermodynamic state variables. In reality, these requirements are very demanding, and it may be difficult or practically, or even theoretically, impossible to satisfy them. This is part of why non-equilibrium thermodynamics is a work in progress.

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==

Some concepts of particular importance for non-equilibrium thermodynamics include time rate of dissipation of energy (Rayleigh 1873,<ref name="Rayleigh 1873">{{Cite journal | last1 = Strutt | first1 = J. W. | doi = 10.1112/plms/s1-4.1.357 | title = Some General Theorems relating to Vibrations | journal = Proceedings of the London Mathematical Society | year = 1871 | volume = s1-4 | pages = 357–368 | url = https://zenodo.org/record/1447754 }}</ref> [[Lars Onsager|Onsager]] 1931,<ref name="Onsager 1931 I">{{Cite journal | doi = 10.1103/PhysRev.37.405 | last1 = Onsager | first1 = L. | year = 1931 | title = Reciprocal relations in irreversible processes, I | url = | journal = Physical Review | volume = 37 | issue = 4| pages = 405–426 |bibcode = 1931PhRv...37..405O | doi-access = free }}</ref> also<ref name="Gyarmati 1970">Gyarmati, I. (1967/1970).</ref><ref name="Lavenda 1978">Lavenda, B.H. (1978). ''Thermodynamics of Irreversible Processes'', Macmillan, London, {{ISBN|0-333-21616-4}}.</ref>), time rate of entropy production (Onsager 1931),<ref name="Onsager 1931 I"/> thermodynamic fields,<ref>Gyarmati, I. (1967/1970), pages 4-14.</ref><ref name="Ziegler 1983">Ziegler, H., (1983). ''An Introduction to Thermomechanics'', North-Holland, Amsterdam, {{ISBN|0-444-86503-9}}.</ref><ref name="Balescu">Balescu, R. (1975). ''Equilibrium and Non-equilibrium Statistical Mechanics'', Wiley-Interscience, New York, {{ISBN|0-471-04600-0}}, Section 3.2, pages 64-72.</ref> [[dissipative structure]],<ref name="G&P 1971"/> and non-linear dynamical structure.<ref name="Lavenda 1978"/>

Some concepts of particular importance for non-equilibrium thermodynamics include time rate of dissipation of energy (Rayleigh 1873,<ref name="Rayleigh 1873">{{Cite journal | last1 = Strutt | first1 = J. W. | doi = 10.1112/plms/s1-4.1.357 | title = Some General Theorems relating to Vibrations | journal = Proceedings of the London Mathematical Society | year = 1871 | volume = s1-4 | pages = 357–368 | url = https://zenodo.org/record/1447754 }}</ref> [[Lars Onsager|Onsager]] 1931,<ref name="Onsager 1931 I">{{Cite journal | doi = 10.1103/PhysRev.37.405 | last1 = Onsager | first1 = L. | year = 1931 | title = Reciprocal relations in irreversible processes, I | url = | journal = Physical Review | volume = 37 | issue = 4| pages = 405–426 |bibcode = 1931PhRv...37..405O | doi-access = free }}</ref> also<ref name="Gyarmati 1970">Gyarmati, I. (1967/1970).</ref><ref name="Lavenda 1978">Lavenda, B.H. (1978). ''Thermodynamics of Irreversible Processes'', Macmillan, London, {{ISBN|0-333-21616-4}}.</ref>), time rate of entropy production (Onsager 1931),<ref name="Onsager 1931 I"/> thermodynamic fields,<ref>Gyarmati, I. (1967/1970), pages 4-14.</ref><ref name="Ziegler 1983">Ziegler, H., (1983). ''An Introduction to Thermomechanics'', North-Holland, Amsterdam, {{ISBN|0-444-86503-9}}.</ref><ref name="Balescu">Balescu, R. (1975). ''Equilibrium and Non-equilibrium Statistical Mechanics'', Wiley-Interscience, New York, {{ISBN|0-471-04600-0}}, Section 3.2, pages 64-72.</ref> [[dissipative structure]],<ref name="G&P 1971"/> and non-linear dynamical structure.<ref name="Lavenda 1978"/>

Some concepts of particular importance for non-equilibrium thermodynamics include time rate of dissipation of energy (Rayleigh 1873, Onsager 1931, also), time rate of entropy production (Onsager 1931), dissipative structure, and non-linear dynamical structure.

Some concepts of particular importance for non-equilibrium thermodynamics include time rate of dissipation of energy (Rayleigh 1873, Onsager 1931, also), time rate of entropy production (Onsager 1931),thermodynamic fields,  dissipative structure,and non-linear dynamical structure.

非平衡态热力学中一些特别重要的概念包括能量耗散的时间速率(Rayleigh 1873，Onsager 1931)，熵产生速率(Onsager 1931)，耗散结构和非线性动力结构。

非平衡态热力学中一些特别重要的概念包括能量耗散的时间速率(Rayleigh 1873，Onsager 1931)、熵产生速率(Onsager 1931)、热力学场、耗散结构和非线性动力结构。

One problem of interest is the thermodynamic study of non-equilibrium steady states, in which entropy production and some flows are non-zero, but there is no time variation of physical variables.

One problem of interest is the thermodynamic study of non-equilibrium steady states, in which entropy production and some flows are non-zero, but there is no time variation of physical variables.

Extended irreversible thermodynamics is a branch of non-equilibrium thermodynamics that goes outside the restriction to the local equilibrium hypothesis. The space of state variables is enlarged by including the fluxes of mass, momentum and energy and eventually higher order fluxes.

Extended irreversible thermodynamics is a branch of non-equilibrium thermodynamics that goes outside the restriction to the local equilibrium hypothesis. The space of state variables is enlarged by including the fluxes of mass, momentum and energy and eventually higher order fluxes.

The formalism is well-suited for describing high-frequency processes and small-length scales materials.

The formalism is well-suited for describing high-frequency processes and small-length scales materials.