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Almost all systems found in nature are not in thermodynamic equilibrium, for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Some systems and processes are, however, in a useful sense, near enough to thermodynamic equilibrium to allow description with useful accuracy by currently known non-equilibrium thermodynamics. Nevertheless, many natural systems and processes will always remain far beyond the scope of non-equilibrium thermodynamic methods due to the existence of non variational dynamics, where the concept of free energy is lost.

Almost all systems found in nature are not in thermodynamic equilibrium, for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Some systems and processes are, however, in a useful sense, near enough to thermodynamic equilibrium to allow description with useful accuracy by currently known non-equilibrium thermodynamics. Nevertheless, many natural systems and processes will always remain far beyond the scope of non-equilibrium thermodynamic methods due to the existence of non variational dynamics, where the concept of free energy is lost.

The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. One fundamental difference between equilibrium thermodynamics and non-equilibrium thermodynamics lies in the behaviour of inhomogeneous systems, which require for their study knowledge of rates of reaction which are not considered in equilibrium thermodynamics of homogeneous systems. This is discussed below. Another fundamental and very important difference is the difficulty or impossibility, in general, in defining entropy at an instant of time in macroscopic terms for systems not in thermodynamic equilibrium; it can be done, to useful approximation, only in carefully chosen special cases, namely those that are throughout in local thermodynamic equilibrium.

The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. One fundamental difference between equilibrium thermodynamics and non-equilibrium thermodynamics lies in the behaviour of inhomogeneous systems, which require for their study knowledge of rates of reaction which are not considered in equilibrium thermodynamics of homogeneous systems. This is discussed below. Another fundamental and very important difference is the difficulty or impossibility, in general, in defining entropy at an instant of time in macroscopic terms for systems not in thermodynamic equilibrium; it can be done, to useful approximation, only in carefully chosen special cases, namely those that are throughout in local thermodynamic equilibrium.

非平衡体系的热力学研究比平衡态热力学研究需要更普适的概念。非平衡态热力学和平衡态热力学之间的一个根本区别在于非均匀系统的行为，这就要求他们研究反应速率的知识，而这一点在均匀系统的平衡态热力学中没有考虑，下面将讨论这一点。另一个基本的和非常重要的区别是，在一般情况下，难以或不可能用宏观量来定义非热力学平衡系统在瞬时的熵; 只有在某些精心选择的特殊情况下加入一些有用的近似才能定义熵，即局部热力学平衡。

对非平衡系统的热力学研究比平衡态热力学研究需要更普适的概念。非平衡态热力学和平衡态热力学之间的一个根本区别在于非均匀系统的行为，这就要求对反应速率有研究，而这一点在均匀系统的平衡态热力学中没有考虑，下面将讨论这一点。另一个基且非常重要的区别是，在一般情况下，很难或者不可能用宏观量来定义非热力学平衡系统在瞬时的熵; 只有在某些精心选择的特殊情况下加入一些有用的近似才能定义熵，即局部热平衡。

A profound difference separates equilibrium from non-equilibrium thermodynamics. Equilibrium thermodynamics ignores the time-courses of physical processes. In contrast, non-equilibrium thermodynamics attempts to describe their time-courses in continuous detail.

A profound difference separates equilibrium from non-equilibrium thermodynamics. Equilibrium thermodynamics ignores the time-courses of physical processes. In contrast, non-equilibrium thermodynamics attempts to describe their time-courses in continuous detail.

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。

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，该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。

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仍在进展中的工作。

定义非平衡热力学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，或者说实际上，甚至理论上都不可能满足。这就部分解释了为什么非平衡态热力学是一个仍在进行的工作。

==Overview 概述==

==Overview 概述==

One initial approach to non-equilibrium thermodynamics is sometimes called 'classical irreversible thermodynamics'. There are other approaches to non-equilibrium thermodynamics, for example extended irreversible thermodynamics, and generalized thermodynamics, but they are hardly touched on in the present article.

One initial approach to non-equilibrium thermodynamics is sometimes called 'classical irreversible thermodynamics'. There are other approaches to non-equilibrium thermodynamics, for example extended irreversible thermodynamics, and generalized thermodynamics, but they are hardly touched on in the present article.

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.

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 （同时参考 Essex）的说法，当前版本的非平衡态热力学忽略了辐射热; 他们之所以可以这样做，是因为他们参照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，它们作为一个整体，不在实验室数量的范围内，那么热辐射就不能被忽视。

根据 Wildt （同时参考 Essex）的说法，当前版本的非平衡态热力学忽略了辐射热; 他们之所以可以这样做，是因为他们参照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以立方公里计的大量物质，它们作为一个整体，不在实验室数量的范围内，那么热辐射就不能被忽视。

The terms 'classical irreversible thermodynamics' 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 is needed in choosing the independent variables 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' 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 is needed in choosing the independent variables 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”有时被用来指非平衡热力学中的一类，它需要如下一些简化的假设。这些假设的效果是使系统的每个非常小的体积元是等效同质的，或者是充分混合的，或者没有有效的空间结构，以及没有体流动能或扩散通量。即使在经典不可逆热力学的思想框架内，在选择系统的独立变量时也需要谨慎。在某些著作中，假设平衡热力学的强度量足够作为任务的独立变量(这些变量被认为没有“记忆”，不显示迟滞现象);特别地，局部流的强度量不允许作为独立变量;局部流被认为依赖于准静态局部强度量。

“经典不可逆热力学”和“局部平衡热力学”有时被用来指代一类非平衡热力学。它需要如下的一些简化假设。这些假设的效果是使系统的每个非常小的体积元是等效同质的，或者是充分混合的，或者没有有效的空间结构，以及没有体流动能或扩散通量。即使在经典不可逆热力学的思想框架内，在选择系统的独立变量时也需要谨慎。在某些著作中，假设平衡热力学的强度量足够作为任务的独立变量(这些变量被认为没有“记忆”，不显示迟滞现象);特别地，局部流的强度量不允许作为独立变量;局部流被认为依赖于准静态局部强度量。