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第65行： − + − According to Wildt (see also Essex), current versions of non-equilibrium thermodynamics ignore radiant heat; they can do so because they refer to laboratory quantities of matter under laboratory conditions with temperatures well below those of stars. At laboratory temperatures, in laboratory quantities of matter, thermal radiation is weak and can be practically nearly ignored. But, for example, atmospheric physics is concerned with large amounts of matter, occupying cubic kilometers, that, taken as a whole, are not within the range of laboratory quantities; then thermal radiation cannot be ignored.+ − − 根据 Wildt 的说法，当前版本的非平衡态热力学星云忽略了辐射热; 它们之所以能做到这一点，是因为它们指的是实验室条件下的物质数量，而实验室条件下的物质温度远低于恒星的温度。在实验室温度下，在实验室数量的物质中，热辐射很弱，几乎可以忽略不计。但是，例如，大气物理学关注的是占据立方公里的大量物质，作为一个整体，不在实验室数量的范围内; 那么热辐射就不能被忽视。 第77行：
第75行： + − The terms 'classical irreversible thermodynamics' for systems. In some writings, it is assumed that the intensive variables of equilibrium thermodynamics are sufficient as the independent variables for the task (such variables are considered to have no 'memory', and do not show hysteresis); in particular, local flow intensive variables are not admitted as independent variables; local flows are considered as dependent on quasi-static local intensive variables. − − 系统的经典不可逆热力学术语。在一些著作中，假定平衡热力学的密集变量充分作为任务的独立变量(这些变量被认为没有”记忆” ，不显示滞后) ; 特别是，局部流密集变量不被承认为独立变量; 局部流被认为是依赖于准静态的局部密集变量。 + − Also it is assumed that the local entropy density is the same function of the other local intensive variables as in equilibrium; this is called the local thermodynamic equilibrium assumption (see also Keizer (1987)). Radiation is ignored because it is transfer of energy between regions, which can be remote from one another. In the classical irreversible thermodynamic approach, there is allowed very small spatial variation, from very small volume element to adjacent very small volume element, but it is assumed that the global entropy of the system can be found by simple spatial integration of the local entropy density; this means that spatial structure cannot contribute as it properly should to the global entropy assessment for the system. This approach assumes spatial and temporal continuity and even differentiability of locally defined intensive variables such as temperature and internal energy density. All of these are very stringent demands. Consequently, this approach can deal with only a very limited range of phenomena. This approach is nevertheless valuable because it can deal well with some macroscopically observable phenomena. − − 同时假设局部熵密度与平衡状态下其他局部密集型变量的函数相同，这被称为局部热力学平衡假设(参见 Keizer (1987))。辐射之所以被忽略，是因为它是能量在区域之间的转移，而区域之间可以相互远离。在经典的不可逆热力学方法中，允许有非常小的空间变化，从非常小的体积元到相邻的非常小的体积元，但是假定系统的总体熵可以通过简单的局部熵密度的空间积分得到，这意味着空间结构不能对系统的总体熵评价作出贡献，因为它应该对系统的总体熵评价作出贡献。这种方法假设空间和时间的连续性，甚至可微的局部定义的强度变量，如温度和内部能量密度。所有这些都是非常严格的要求。因此，这种方法只能处理非常有限范围的现象。然而，这种方法是有价值的，因为它可以很好地处理一些宏观上可观察到的现象。 + − In other writings, local flow variables are considered; these might be considered as classical by analogy with the time-invariant long-term time-averages of flows produced by endlessly repeated cyclic processes; examples with flows are in the thermoelectric phenomena known as the Seebeck and the Peltier effects, considered by Kelvin in the nineteenth century and by Lars Onsager in the twentieth. These effects occur at metal junctions, which were originally effectively treated as two-dimensional surfaces, with no spatial volume, and no spatial variation. − 在其他著作中，考虑了局部流动变量; 这些可以被认为是经典的，类比于由无休止的重复循环过程产生的流动的时不变的长期时间平均值; 有关流动的例子是被称为 Seebeck 和 Peltier 效应的热电现象，开尔文在十九世纪和拉斯昂萨格尔在二十世纪考虑。这些效应发生在金属连接处，最初被有效地处理为二维表面，没有空间体积，也没有空间变化。+ − − + − A further extension of local equilibrium thermodynamics is to allow that materials may have "memory", so that their constitutive equations depend not only on present values but also on past values of local equilibrium variables. Thus time comes into the picture more deeply than for time-dependent local equilibrium thermodynamics with memoryless materials, but fluxes are not independent variables of state.+ − − 局域平衡热力学的进一步扩展是允许材料具有”记忆” ，因此它们的本构方程不仅依赖于现值，而且依赖于局域平衡变量的过去值。因此，对于无记忆材料，时间比依赖时间的局域平衡热力学更为深入，但是通量并不是状态的独立变量。 − − + − 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. − − 扩展不可逆热力学是非平衡态热力学热力学的一个分支，它超越了局部平衡假说的限制。状态变量的空间通过包括质量、动量和能量的通量以及最终的高阶通量来扩大。 − The formalism is well-suited for describing high-frequency processes and small-length scales materials.+ − − 形式主义非常适合于描述高频过程和小尺度材料。 第129行：
第114行： + − 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. − − 有许多固定的非平衡系统的例子，其中一些非常简单，例如在不同温度下被限制在两个恒温器之间的系统，或普通的 Couette 流动，两个平板壁之间的流体沿相反方向运动，并定义了壁上的非平衡条件。激光作用也是一个非平衡过程，但它依赖于脱离局部热力学平衡，因此超出了经典不可逆热力学的范围; 在这里，两个分子自由度(分子激光、振动和转动分子运动)之间保持了很大的温差，在一个很小的空间区域需要两个分量的‘温度’ ，排除了局部热力学平衡，这就要求只需要一个温度。声扰动或激波的阻尼是非平稳的非平衡过程。被驱动的复杂流体、湍流系统和玻璃是非平衡系统的其他例子。 − − ====Local equilibrium thermodynamics with materials with "memory"==== + − The mechanics of macroscopic systems depends on a number of extensive quantities. It should be stressed that all systems are permanently interacting with their surroundings, thereby causing unavoidable fluctuations of extensive quantities. Equilibrium conditions of thermodynamic systems are related to the maximum property of the entropy. If the only extensive quantity that is allowed to fluctuate is the internal energy, all the other ones being kept strictly constant, the temperature of the system is measurable and meaningful. The system's properties are then most conveniently described using the thermodynamic potential Helmholtz free energy (A = U - TS), a Legendre transformation of the energy. If, next to fluctuations of the energy, the macroscopic dimensions (volume) of the system are left fluctuating, we use the Gibbs free energy (G = U + PV - TS), where the system's properties are determined both by the temperature and by the pressure.+ − 宏观系统的力学依赖于大量的数据。应当强调的是，所有系统都与其周围环境永久地相互作用，从而造成大量不可避免的波动。热力学系统的平衡条件与熵的最大性质有关。如果唯一允许大范围波动的量是内能，而其它量都严格保持恒定，那么系统的温度就是可测量的，也是有意义的。系统的性质可以用热动力位能亥姆霍兹自由能(a = u-TS)来描述，它是能量的勒壤得转换。如果除了能量的波动，系统的宏观尺寸(体积)仍然保持波动状态，我们使用吉布斯自由能(g = u + PV-TS) ，其中系统的性质既由温度决定，也由压力决定。 + − ===Extended irreversible thermodynamics===+ − Non-equilibrium systems are much more complex and they may undergo fluctuations of more extensive quantities. The boundary conditions impose on them particular intensive variables, like temperature gradients or distorted collective motions (shear motions, vortices, etc.), often called thermodynamic forces. If free energies are very useful in equilibrium thermodynamics, it must be stressed that there is no general law defining stationary non-equilibrium properties of the energy as is the second law of thermodynamics for the entropy in equilibrium thermodynamics. That is why in such cases a more generalized Legendre transformation should be considered. This is the extended Massieu potential.+ − 非平衡系统要复杂得多，它们可能经历更广泛的量的波动。边界条件强加给它们特殊的强度变量，如温度梯度或扭曲的集体运动(剪切运动、涡旋等)。) ，通常称为热力学力。如果自由能在平衡态热力学中非常有用，那么必须强调的是，在平衡态热力学中，定义能量的稳态非平衡性质的一般定律，并不像平衡态热力学中熵的热力学第二定律定律那样。这就是为什么在这种情况下，应该考虑一个更广泛的勒壤得转换。这就是延伸的马西欧势。 − '''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 [[flux]]es of mass, momentum and energy and eventually higher order fluxes. − − By definition, the entropy (S) is a function of the collection of extensive quantities <math>E_i</math>. Each extensive quantity has a conjugate intensive variable <math>I_i</math> (a restricted definition of intensive variable is used here by comparison to the definition given in this link) so that: − − 根据定义，熵(s)是大量集合的函数。每个扩展量都有一个共轭密集变量 i _ i </math > (通过与本链接中给出的定义进行比较，这里使用了密集变量的有限定义) ，因此: − + − − − <math> I_i = \frac{\partial{S}}{\partial{E_i}}.</math> − − [数学] i = frac { partial { s }{ e _ i }
→Overview
定义非平衡热力学状态变量的关系如下：在系统恰好处于很接近热力学平衡状态的情况下，非平衡状态变量可以通过与测量热力学状态变量相同的技术，或通过相应的时空导数，包括物质和能量通量，以足够的精度在本地进行测量。通常，非平衡热力学系统在空间和时间上都是非均匀的，但是它们的非均匀性仍然具有足够的平滑度，以保证非平衡状态变量的时空导数适当存在。另外由于空间的不均匀性，必须将非平衡状态变量（对应于广义热力学状态变量）定义为相应的广义平衡状态变量的空间密度。在系统足够接近热力学平衡的情况下，密集的非平衡状态变量（例如温度和压力）与平衡状态变量紧密对应。测量时探头必须足够小，并且响应速度要足够快，以捕获相关的不均匀性。此外，要求非平衡状态变量在数学上彼此函数相关，其方式应类似于平衡热力学状态变量之间的对应关系。实际上，这些要求非常苛刻，可能很难实现，或实际上，甚至在理论上无法满足它们。这就是非平衡热力学的研究一直处在探索中的部分原因。
定义非平衡热力学状态变量的关系如下：在系统恰好处于很接近热力学平衡状态的情况下，非平衡状态变量可以通过与测量热力学状态变量相同的技术，或通过相应的时空导数，包括物质和能量通量，以足够的精度在本地进行测量。通常，非平衡热力学系统在空间和时间上都是非均匀的，但是它们的非均匀性仍然具有足够的平滑度，以保证非平衡状态变量的时空导数适当存在。另外由于空间的不均匀性，必须将非平衡状态变量（对应于广义热力学状态变量）定义为相应的广义平衡状态变量的空间密度。在系统足够接近热力学平衡的情况下，密集的非平衡状态变量（例如温度和压力）与平衡状态变量紧密对应。测量时探头必须足够小，并且响应速度要足够快，以捕获相关的不均匀性。此外，要求非平衡状态变量在数学上彼此函数相关，其方式应类似于平衡热力学状态变量之间的对应关系。实际上，这些要求非常苛刻，可能很难实现，或实际上，甚至在理论上无法满足它们。这就是非平衡热力学的研究一直处在探索中的部分原因。
==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.
非平衡热力学目前仍然处在探索中，距离理论成熟仍需要一定时间。本文试图勾勒出一些方法和一些重要的概念。
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"/>
对于非平衡热力学，特别重要的一些概念包括：能量耗散的时间速率（Rayleigh 1873，Onsager 1931），熵产生的时间速率（Onsager 1931），热力学场，'''<font color="#ff8000"> 耗散结构Dissipative structure</font>'''和非线性动力学结构。
One problem of interest is the thermodynamic study of non-equilibrium [[steady state]]s, in which [[entropy]] production and some [[flux|flows]] are non-zero, but there is no [[Time-variant system|time variation]] of physical variables.
One problem of interest is the thermodynamic study of non-equilibrium [[steady state]]s, in which [[entropy]] production and some [[flux|flows]] are non-zero, but there is no [[Time-variant system|time variation]] of physical variables.
感兴趣的问题之一是对'''<font color="#ff8000"> 非平衡稳态Non-equilibrium steady states</font>'''的热力学研究，其中包括熵产生，和某些非零流量，不过这些物理变量不具有时间变化性。
One initial approach to non-equilibrium thermodynamics is sometimes called 'classical irreversible thermodynamics'.<ref name="Lebon Jou Casas-Vázquez 2008"/> There are other approaches to non-equilibrium thermodynamics, for example [[extended irreversible thermodynamics]],<ref name="Lebon Jou Casas-Vázquez 2008"/><ref name="JCVL 1993"/> and generalized thermodynamics,<ref>Eu, B.C. (2002).</ref> but they are hardly touched on in the present article.
One initial approach to non-equilibrium thermodynamics is sometimes called 'classical irreversible thermodynamics'.<ref name="Lebon Jou Casas-Vázquez 2008"/> There are other approaches to non-equilibrium thermodynamics, for example [[extended irreversible thermodynamics]],<ref name="Lebon Jou Casas-Vázquez 2008"/><ref name="JCVL 1993"/> and generalized thermodynamics,<ref>Eu, B.C. (2002).</ref> but they are hardly touched on in the present article.
有一种分析非平衡热力学的初始方法被称为“'''<font color="#ff8000"> 经典不可逆热力学Classical irreversible thermodynamics</font>'''”。同时还有其他方法例如：'''<font color="#ff8000"> 扩展的不可逆热力学Extended irreversible thermodynamics</font>'''和'''<font color="#ff8000"> 广义热力学Generalized thermodynamics</font>'''，但在本文中几乎没有涉及。
=== Quasi-radiationless non-equilibrium thermodynamics of matter in laboratory conditions 实验室条件下物质的准无辐射非平衡热力学 ===
===Quasi-radiationless non-equilibrium thermodynamics of matter in laboratory conditions===
According to Wildt<ref name="Wildt 1972">{{Cite journal |last=Wildt |first=R. |year=1972 |title=Thermodynamics of the gray atmosphere. IV. Entropy transfer and production |journal=Astrophysical Journal |volume=174 |issue= |pages=69–77 |doi=10.1086/151469 |bibcode=1972ApJ...174...69W}}</ref> (see also Essex<ref name="Essex 1984a">{{Cite journal |last=Essex |first=C. |year=1984a |title=Radiation and the irreversible thermodynamics of climate |journal=Journal of the Atmospheric Sciences |volume=41 |issue=12 |pages=1985–1991 |doi=10.1175/1520-0469(1984)041<1985:RATITO>2.0.CO;2 |bibcode = 1984JAtS...41.1985E |doi-access=free }}.</ref><ref name="Essex 1984b">{{Cite journal |last=Essex |first=C. |year=1984b |title=Minimum entropy production in the steady state and radiative transfer |journal=Astrophysical Journal |volume=285 |issue= |pages=279–293 |doi=10.1086/162504 |bibcode=1984ApJ...285..279E}}</ref><ref name="Essex 1984c">{{Cite journal |last=Essex |first=C. |year=1984c |title=Radiation and the violation of bilinearity in the irreversible thermodynamics of irreversible processes |journal=Planetary and Space Science |volume=32 |pages=1035–1043 |doi=10.1016/0032-0633(84)90060-6 |bibcode = 1984P&SS...32.1035E |issue=8 }}</ref>), current versions of non-equilibrium thermodynamics ignore radiant heat; they can do so because they refer to laboratory quantities of matter under laboratory conditions with temperatures well below those of stars. At laboratory temperatures, in laboratory quantities of matter, thermal radiation is weak and can be practically nearly ignored. But, for example, atmospheric physics is concerned with large amounts of matter, occupying cubic kilometers, that, taken as a whole, are not within the range of laboratory quantities; then thermal radiation cannot be ignored.
According to Wildt<ref name="Wildt 1972">{{Cite journal |last=Wildt |first=R. |year=1972 |title=Thermodynamics of the gray atmosphere. IV. Entropy transfer and production |journal=Astrophysical Journal |volume=174 |issue= |pages=69–77 |doi=10.1086/151469 |bibcode=1972ApJ...174...69W}}</ref> (see also Essex<ref name="Essex 1984a">{{Cite journal |last=Essex |first=C. |year=1984a |title=Radiation and the irreversible thermodynamics of climate |journal=Journal of the Atmospheric Sciences |volume=41 |issue=12 |pages=1985–1991 |doi=10.1175/1520-0469(1984)041<1985:RATITO>2.0.CO;2 |bibcode = 1984JAtS...41.1985E |doi-access=free }}.</ref><ref name="Essex 1984b">{{Cite journal |last=Essex |first=C. |year=1984b |title=Minimum entropy production in the steady state and radiative transfer |journal=Astrophysical Journal |volume=285 |issue= |pages=279–293 |doi=10.1086/162504 |bibcode=1984ApJ...285..279E}}</ref><ref name="Essex 1984c">{{Cite journal |last=Essex |first=C. |year=1984c |title=Radiation and the violation of bilinearity in the irreversible thermodynamics of irreversible processes |journal=Planetary and Space Science |volume=32 |pages=1035–1043 |doi=10.1016/0032-0633(84)90060-6 |bibcode = 1984P&SS...32.1035E |issue=8 }}</ref>), current versions of non-equilibrium thermodynamics ignore radiant heat; they can do so because they refer to laboratory quantities of matter under laboratory conditions with temperatures well below those of stars. At laboratory temperatures, in laboratory quantities of matter, thermal radiation is weak and can be practically nearly ignored. But, for example, atmospheric physics is concerned with large amounts of matter, occupying cubic kilometers, that, taken as a whole, are not within the range of laboratory quantities; then thermal radiation cannot be ignored.
怀尔德Wild（也参见Essex）认为，当前版本的非平衡热力学忽略了辐射热；之所以可以这么做，是因为它们的研究对象是实验室条件下，温度远低于星体温度的实验室物质量。在实验室温度下，基于实验室物质量，其热辐射非常微弱，几乎可以忽略不计。但是，例如大气物理学中涉及的大量物质，他们占有立方公里的空间，总体上讲，不属于实验室数量范围内；那么其热辐射就不能忽略。
=== Local equilibrium thermodynamics 局部平衡热力学 ===
===Local equilibrium thermodynamics===
The terms 'classical irreversible thermodynamics'<ref name="Lebon Jou Casas-Vázquez 2008"/> and 'local equilibrium thermodynamics' are sometimes used to refer to a version of non-equilibrium thermodynamics that demands certain simplifying assumptions, as follows. The assumptions have the effect of making each very small volume element of the system effectively homogeneous, or well-mixed, or without an effective spatial structure, and without kinetic energy of bulk flow or of diffusive flux. Even within the thought-frame of classical irreversible thermodynamics, care<ref name="Lavenda 1978"/> is needed in choosing the independent variables<ref>Prigogine, I., Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London, page 1.</ref> for systems. In some writings, it is assumed that the intensive variables of equilibrium thermodynamics are sufficient as the independent variables for the task (such variables are considered to have no 'memory', and do not show hysteresis); in particular, local flow intensive variables are not admitted as independent variables; local flows are considered as dependent on quasi-static local intensive variables.
The terms 'classical irreversible thermodynamics'<ref name="Lebon Jou Casas-Vázquez 2008"/> and 'local equilibrium thermodynamics' are sometimes used to refer to a version of non-equilibrium thermodynamics that demands certain simplifying assumptions, as follows. The assumptions have the effect of making each very small volume element of the system effectively homogeneous, or well-mixed, or without an effective spatial structure, and without kinetic energy of bulk flow or of diffusive flux. Even within the thought-frame of classical irreversible thermodynamics, care<ref name="Lavenda 1978"/> is needed in choosing the independent variables<ref>Prigogine, I., Defay, R. (1950/1954). ''Chemical Thermodynamics'', Longmans, Green & Co, London, page 1.</ref> for systems. In some writings, it is assumed that the intensive variables of equilibrium thermodynamics are sufficient as the independent variables for the task (such variables are considered to have no 'memory', and do not show hysteresis); in particular, local flow intensive variables are not admitted as independent variables; local flows are considered as dependent on quasi-static local intensive variables.
术语“经典不可逆热力学”和“局部平衡热力学”有时用于指代那些需要简化假设的非平衡热力学。这些假设的作用是使系统中每个非常小体积的元素能有效地均质化，或混合充分，或无有效的空间结构，同时也没有大流量或扩散通量的动能。即使在经典不可逆热力学的思想框架内，在选择系统的自变量时也需要谨慎。在某些著作中，假设平衡热力学的密集变量足以作为研究的自变量（此类变量被认为没有“内存”，并且不显示迟滞）；不允许将局部流量密集型变量视为自变量；本地流量被认为依赖于准静态局部集约变量。
Also it is assumed that the local entropy density is the same function of the other local intensive variables as in equilibrium; this is called the local thermodynamic equilibrium assumption<ref name="Gyarmati 1970"/><ref name="Lavenda 1978"/><ref name="G&P 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability, and Fluctuations'', Wiley-Interscience, London, 1971, {{ISBN|0-471-30280-5}}.</ref><ref name="JCVL 1993">Jou, D., Casas-Vázquez, J., Lebon, G. (1993). ''Extended Irreversible Thermodynamics'', Springer, Berlin, {{ISBN|3-540-55874-8}}, {{ISBN|0-387-55874-8}}.</ref><ref name="De Groot Mazur 1962">De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam.</ref><ref name="Balescu 1975">Balescu, R. (1975). ''Equilibrium and Non-equilibrium Statistical Mechanics'', John Wiley & Sons, New York, {{ISBN|0-471-04600-0}}.</ref><ref name="Mihalas Mihalas 1984">[http://www.filestube.com/9c5b2744807c2c3d03e9/details.html Mihalas, D., Weibel-Mihalas, B. (1984). ''Foundations of Radiation Hydrodynamics'', Oxford University Press, New York] {{ISBN|0-19-503437-6}}.</ref><ref name="Schloegl 1989">Schloegl, F. (1989). ''Probability and Heat: Fundamentals of Thermostatistics'', Freidr. Vieweg & Sohn, Braunschweig, {{ISBN|3-528-06343-2}}.</ref> (see also Keizer (1987)<ref name="Keizer 1987">Keizer, J. (1987). ''Statistical Thermodynamics of Nonequilibrium Processes'', Springer-Verlag, New York, {{ISBN|0-387-96501-7}}.</ref>). Radiation is ignored because it is transfer of energy between regions, which can be remote from one another. In the classical irreversible thermodynamic approach, there is allowed very small spatial variation, from very small volume element to adjacent very small volume element, but it is assumed that the global entropy of the system can be found by simple spatial integration of the local entropy density; this means that spatial structure cannot contribute as it properly should to the global entropy assessment for the system. This approach assumes spatial and temporal continuity and even differentiability of locally defined intensive variables such as temperature and internal energy density. All of these are very stringent demands. Consequently, this approach can deal with only a very limited range of phenomena. This approach is nevertheless valuable because it can deal well with some macroscopically observable phenomena.{{examples|date=February 2015}}
Also it is assumed that the local entropy density is the same function of the other local intensive variables as in equilibrium; this is called the local thermodynamic equilibrium assumption<ref name="Gyarmati 1970"/><ref name="Lavenda 1978"/><ref name="G&P 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability, and Fluctuations'', Wiley-Interscience, London, 1971, {{ISBN|0-471-30280-5}}.</ref><ref name="JCVL 1993">Jou, D., Casas-Vázquez, J., Lebon, G. (1993). ''Extended Irreversible Thermodynamics'', Springer, Berlin, {{ISBN|3-540-55874-8}}, {{ISBN|0-387-55874-8}}.</ref><ref name="De Groot Mazur 1962">De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North-Holland, Amsterdam.</ref><ref name="Balescu 1975">Balescu, R. (1975). ''Equilibrium and Non-equilibrium Statistical Mechanics'', John Wiley & Sons, New York, {{ISBN|0-471-04600-0}}.</ref><ref name="Mihalas Mihalas 1984">[http://www.filestube.com/9c5b2744807c2c3d03e9/details.html Mihalas, D., Weibel-Mihalas, B. (1984). ''Foundations of Radiation Hydrodynamics'', Oxford University Press, New York] {{ISBN|0-19-503437-6}}.</ref><ref name="Schloegl 1989">Schloegl, F. (1989). ''Probability and Heat: Fundamentals of Thermostatistics'', Freidr. Vieweg & Sohn, Braunschweig, {{ISBN|3-528-06343-2}}.</ref> (see also Keizer (1987)<ref name="Keizer 1987">Keizer, J. (1987). ''Statistical Thermodynamics of Nonequilibrium Processes'', Springer-Verlag, New York, {{ISBN|0-387-96501-7}}.</ref>). Radiation is ignored because it is transfer of energy between regions, which can be remote from one another. In the classical irreversible thermodynamic approach, there is allowed very small spatial variation, from very small volume element to adjacent very small volume element, but it is assumed that the global entropy of the system can be found by simple spatial integration of the local entropy density; this means that spatial structure cannot contribute as it properly should to the global entropy assessment for the system. This approach assumes spatial and temporal continuity and even differentiability of locally defined intensive variables such as temperature and internal energy density. All of these are very stringent demands. Consequently, this approach can deal with only a very limited range of phenomena. This approach is nevertheless valuable because it can deal well with some macroscopically observable phenomena.{{examples|date=February 2015}}
同时还假设局部熵密度与热力学平衡中的其他局部强度变量的函数相同。这称为局部热力学平衡假设（另请参见Keizer（1987）。需要注意的是辐射被忽略了，因为它是区域之间的能量转移，而这些区域可能彼此远离。在经典的不可逆热力学方法中，允许非常小的空间变化，从很小的体积元素到相邻的很小的体积元素，但是是基于假设可以将局部熵密度进行简单的空间积分来找到系统的全局熵的。这意味着空间结构无法适当地为系统全局熵的评估做出贡献。这种方法假设了空间和时间的连续性，甚至假设了局部定义的强度变量（例如温度和内部能量密度）的可微性。所有这些都是非常严格的要求。因此，这种方法只能处理非常有限的现象。不过这种方法很有价值，因为它可以很好地处理一些宏观上可观察到的现象。
In other writings, local flow variables are considered; these might be considered as classical by analogy with the time-invariant long-term time-averages of flows produced by endlessly repeated cyclic processes; examples with flows are in the [[thermoelectric effect|thermoelectric phenomena]] known as the Seebeck and the Peltier effects, considered by [[William Thomson, 1st Baron Kelvin|Kelvin]] in the nineteenth century and by [[Lars Onsager]] in the twentieth.<ref name="De Groot Mazur 1962"/><ref>Kondepudi, D. (2008). ''Introduction to Modern Thermodynamics'', Wiley, Chichester UK, {{ISBN|978-0-470-01598-8}}, pages 333-338.</ref> These effects occur at metal junctions, which were originally effectively treated as two-dimensional surfaces, with no spatial volume, and no spatial variation.
In other writings, local flow variables are considered; these might be considered as classical by analogy with the time-invariant long-term time-averages of flows produced by endlessly repeated cyclic processes; examples with flows are in the [[thermoelectric effect|thermoelectric phenomena]] known as the Seebeck and the Peltier effects, considered by [[William Thomson, 1st Baron Kelvin|Kelvin]] in the nineteenth century and by [[Lars Onsager]] in the twentieth.<ref name="De Groot Mazur 1962"/><ref>Kondepudi, D. (2008). ''Introduction to Modern Thermodynamics'', Wiley, Chichester UK, {{ISBN|978-0-470-01598-8}}, pages 333-338.</ref> These effects occur at metal junctions, which were originally effectively treated as two-dimensional surfaces, with no spatial volume, and no spatial variation.
在其他研究著作中，还考虑了局部流动变量。其经典思想是将局部热量认为是通过不断循环产生的长效定常时均的流量，其相关例子如'''<font color="#ff8000"> 热电现象Thermoelectric phenomena</font>'''，即'''<font color="#ff8000"> 塞贝克效应Seebeck effect</font>'''和'''<font color="#ff8000"> 珀尔帖效应Peltier effect</font>'''，由开尔文Kelvin在19世纪和拉尔斯·昂萨格Lars Onsager在20世纪提出。这些效应发生在金属链接处，这些链接最初被有效地视为二维表面，没有空间体积，也没有空间变化。
==== Local equilibrium thermodynamics with materials with "memory" 具有“记忆”材料的局部平衡热力学 ====
A further extension of local equilibrium thermodynamics is to allow that materials may have "memory", so that their [[constitutive equation]]s depend not only on present values but also on past values of local equilibrium variables. Thus time comes into the picture more deeply than for time-dependent local equilibrium thermodynamics with memoryless materials, but fluxes are not independent variables of state.<ref>{{cite journal | last1 = Coleman | first1 = B.D. | last2 = Noll | first2 = W. | year = 1963 | title = The thermodynamics of elastic materials with heat conduction and viscosity | url = | journal = Arch. Ration. Mach. Analysis | volume = 13 | issue = 1| pages = 167–178 | doi=10.1007/bf01262690| bibcode = 1963ArRMA..13..167C | s2cid = 189793830 }}</ref>
A further extension of local equilibrium thermodynamics is to allow that materials may have "memory", so that their [[constitutive equation]]s depend not only on present values but also on past values of local equilibrium variables. Thus time comes into the picture more deeply than for time-dependent local equilibrium thermodynamics with memoryless materials, but fluxes are not independent variables of state.<ref>{{cite journal | last1 = Coleman | first1 = B.D. | last2 = Noll | first2 = W. | year = 1963 | title = The thermodynamics of elastic materials with heat conduction and viscosity | url = | journal = Arch. Ration. Mach. Analysis | volume = 13 | issue = 1| pages = 167–178 | doi=10.1007/bf01262690| bibcode = 1963ArRMA..13..167C | s2cid = 189793830 }}</ref>
局部平衡热力学的进一步扩展是允许材料具有“记忆”，因此它们的'''<font color="#ff8000"> 本构方程Constitutive equations</font>'''不仅取决于局部平衡变量的当前值，而且还取决于过去的值。因此，与无记忆材料的依时性局部平衡热力学相比，时间对图像的影响更深，不过通量不是状态的独立变量。
=== Extended irreversible thermodynamics 扩展的不可逆热力学 ===
'''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 [[flux]]es of mass, momentum and energy and eventually higher order fluxes.
扩展的不可逆热力学是非平衡热力学的一个分支，它超出了局部平衡假设的限制。通过包括质量，动量和能量通量以及最终的高阶通量来扩大状态变量的空间。
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.
该形式体系非常适合描述高频过程和小尺度材料。
==Basic concepts==
==Basic concepts==