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==Thermodynamic state of internal equilibrium of a system==

==Thermodynamic state of internal equilibrium of a system==

 

A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)

A collection of matter may be entirely isolated from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its more customary definition, which apparently was suggested by Fowler.)

物质的集合可能与其周围的环境完全分离。如果它一直保持不受干扰的无限长的时间，经典热力学假定，它是在一个状态，其中没有发生任何变化，其中没有流动。这是内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律，但并不常见。一本教科书称之为“第零定律” ，并指出作者认为这个定义比较符合书名的习惯定义，后者显然是由福勒提出的。)

物质的集合可能与其周围的环境完全'''<font color="#ff8000">孤立 Isolated</font>'''。如果它在无限长的时间内一直保持不受干扰，经典热力学假定，它是在一个没有发生任何变化，没有流动的状态。这是内部平衡的热力学状态。(这种假设有时被称为“负第一”热力学定律，但并不常见。一本教科书称之为“第零定律” ，并指出作者认为这个标题是'''<font color="#ff8000">更符合惯例的定义 More Customary Definition</font>'''，后者显然是由'''<font color="#ff8000">福勒 Fowler</font>'''提出的。)

Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.

Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a thermodynamic operation be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.

==Multiple contact equilibrium==

==Multiple contact equilibrium==

 

A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring  within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to  the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.

A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring  within a definitely limited time. For example, an immovable adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to  the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural thermodynamic process. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of "inanimate" agency; a system in thermodynamic equilibrium is inanimate.

热力学操作可能作为一个事件发生在周围环境的墙壁上，既不直接影响与周围环境联系的墙壁，也不直接影响其内部，并且发生在一个明确的有限的时间内。例如，一个固定的绝热壁可以在环境中放置或拆除。由于这种操作仅限于周围环境，系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。然后，根据热力学第二定律的说法，整体经历了变化，并最终与周围环境达到了新的最终平衡。继普朗克之后，这一连串的事件被称为自然热力学过程。这在平衡态热力学中是允许的，因为初始状态和最终状态都是热力学平衡的，即使在这个过程中，当系统和周围环境都不处于明确的内部平衡状态时，存在着暂时偏离热力学平衡的现象。一个自然过程在其主要过程中以有限的速度进行。因此，它从根本上不同于虚构的准静态“过程” ，后者在整个过程中无限缓慢地进行，而且虚构的“可逆”。经典热力学允许，即使一个过程可能需要很长的时间才能达到热力学平衡，如果它的主要部分的过程是在一个有限的比率，那么它被认为是自然的，并受制于热力学第二定律，因此是不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。这样的操作和装置在周围环境中而不是在系统中的允许，是 Kelvin 在他的一个热力学第二定律的陈述中提到“无生命的”机构的原因; 在热力学平衡的系统是无生命的。

热力学操作可能作为一个事件发生在周围环境的墙壁上，既不直接影响与周围环境联系的墙壁，也不直接影响其内部，并且发生在一个明确的有限的时间内。例如，一个固定的绝热壁可以在环境中放置或拆除。由于这种操作仅限于周围环境，系统可能会在一段时间内远离自身最初的内部状态---- 热力学平衡。然后，根据热力学第二定律的说法，整体经历了变化，并最终与周围环境达到了新的最终平衡。继普朗克之后，这一连串的事件被称为自然'''<font color="#ff8000">热力学过程 Thermodynamic Process</font>'''。这在平衡态热力学中是允许的，因为初始状态和最终状态都是热力学平衡的，即使在这个过程中，当系统和周围环境都不处于明确的内部平衡状态时，存在着暂时偏离热力学平衡的现象。一个自然过程在其主要过程中以有限的速度进行。因此，它从根本上不同于虚构的准静态“过程” ，后者在整个过程中无限缓慢地进行，而且虚构的“可逆”。经典热力学允许，即使一个过程可能需要很长的时间才能达到热力学平衡，如果它的主要部分的过程是在一个有限的比率，那么它被认为是自然的，并受制于热力学第二定律，因此是不可逆的。工程设计的机器、人工设备和操作是允许在周围环境中进行的。这样的操作和装置在周围环境中而不是在系统中的允许，是 开尔文在他的一个热力学第二定律的陈述中提到'''<font color="#ff8000">无生命机构 Inanimate Agency</font>'''的原因; 在热力学平衡的系统是无生命的。

== Local and global equilibrium ==

== Local and global equilibrium ==

 

It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.

It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters. As an example, temperature controls heat exchanges. Global thermodynamic equilibrium (GTE) means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.

区分全球性和本地性热力学平衡是很有用的。在热力学中，系统内部和系统与外部之间的交换是由密集的参数控制的。例如，温度控制热交换。全球热力学平衡(GTE)意味着这些密集参数在整个系统中是均匀的，而局部热力学平衡(LTE)意味着这些密集参数在空间和时间上是变化的，但变化如此缓慢，以至于对于任何一点，人们都可以假设在某个邻近的某个热力学平衡。

区分全局性和局部性热力学平衡是很有用的。在热力学中，系统内部和系统与外部之间的交换是由'''<font color="#ff8000">密集的 Intensive</font>'''参数控制的。例如，'''<font color="#ff8000"温度 Temperature</font>'''控制'''<font color="#ff8000">热交换 Heat Equation</font>'''。全局热力学平衡(GTE)意味着这些'''<font color="#ff8000">密集的 Intensive</font>'''参数在整个系统中是均匀的，而局部热力学平衡(LTE)意味着这些密集参数在空间和时间上是变化的，但变化如此缓慢，以至于对于任何一点，人们都可以假设在某个邻近的某个热力学平衡。

If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no  LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.

If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no  LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.

如果对系统的描述要求密集参数的变化过大，那么这些密集参数的定义所依据的假设本身就会破裂，系统将既不处于全球平衡，也不处于局部平衡。例如，一个粒子需要一定数量的碰撞才能平衡到它的周围。如果在这些碰撞中移动的平均距离使它离开平衡的邻近区域，它将永远不会平衡，也就不会有 LTE。根据定义，温度与达到平衡的附近区域的平均内能成正比。由于没有达到平衡的邻域，温度的概念就不成立，温度也就变得不确定。

如果对系统的描述要求密集参数的变化过大，那么这些密集参数的定义所依据的假设本身就会破裂，系统将既不处于全局平衡，也不处于局部平衡。例如，一个粒子需要一定数量的碰撞才能平衡到它的周围。如果在这些碰撞中移动的平均距离使它离开平衡的邻近区域，它将永远不会平衡，也就不会有 LTE。根据定义，温度与达到平衡的附近区域的平均内能成正比。由于没有达到平衡的邻域，温度的概念就不成立，温度也就变得不确定。

It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[mass]]ive particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.

It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to [[massive]] particles. In a [[radiation|radiating]] gas, the [[photon]]s being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.

It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.

It is important to note that this local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas doesn't need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE to exist.

值得注意的是，这种局部平衡可能只适用于系统中的某个粒子子集。例如，LTE 通常只适用于大质量粒子。在辐射气体中，被气体发射和吸收的光子不需要彼此在一个热力学平衡内，也不需要与气体中的大量粒子在一起，LTE 才能存在。在某些情况下，自由电子并不需要与大得多的原子或分子处于平衡状态，LTE 才能存在。

值得注意的是，这种局部平衡可能只适用于系统中的某个粒子子集。例如，LTE 通常只适用于'''<font color="#ff8000">大 Massive</font>'''质量粒子。在'''<font color="#ff8000">辐射 Radiation</font>'''气体中，被气体发射和吸收的'''<font color="#ff8000">光子 Photon</font>'''不需要彼此在一个热力学平衡内，也不需要与气体中的大量粒子在一起，LTE 才能存在。在某些情况下，自由电子并不需要与大得多的原子或分子处于平衡状态，LTE 才能存在。

As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.

As an example, LTE will exist in a glass of water that contains a melting ice cube. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature.

举个例子，LTE 将存在于一个装有融化的冰块的水杯中。玻璃杯内的温度可以在任何时候定义，但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量，它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量，它们将按照麦克斯韦-波兹曼分布分布到另一个温度。

举个例子，LTE 将存在于一个装有融化的'''<font color="#ff8000">冰块 Ice Cube</font>'''的水杯中。玻璃杯内的温度可以在任何时候定义，但是离冰块近的地方要比离冰块远的地方冷。如果观察到位于给定点附近的分子的能量，它们将按照麦克斯韦-波兹曼分布在一定温度下的分布。如果观察到位于另一点附近的分子的能量，它们将按照'''<font color="#ff8000">麦克斯韦-波兹曼分布 Maxwell–Boltzmann distribution</font>'''分布到另一个温度。

Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.

Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.

本地热力学平衡不需要本地或全球的平稳性。换句话说，每一个小的地方不需要有一个恒定的温度。然而，它确实要求每个小的局部变化足够缓慢，以实际上维持其局部麦克斯韦-波兹曼分布的分子速度。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如，一个全球稳定的定态可以通过不断地加入精细的冰粉以补偿融化，并不断地排出融化的水来维持在水杯里。自然迁移现象可能导致一个从局部到全球的热力学平衡系统。回到我们的例子，热量的扩散将导致我们的玻璃杯水流向全球热力学平衡，在这种状态下，玻璃杯的温度是完全均匀的。

局部热力学平衡不需要局部或全局的平稳性。换句话说，每一个小的地方不需要有一个恒定的温度。然而，它确实要求每个小的局部变化足够缓慢，以实际上维持其局部麦克斯韦-波兹曼分布的分子速度。全局非平衡态只有通过系统与外界的交换才能保持稳定。例如，一个全局稳定的定态可以通过不断地加入精细的冰粉以补偿融化，并不断地排出融化的水来维持在水杯里。自然'''<font color="#ff8000">迁移现象 Transport Phenomena</font>'''可能导致一个从局部到全局的热力学平衡系统。回到我们的例子，热量的扩散将导致我们的玻璃杯水流向全球热力学平衡，在这种状态下，玻璃杯的温度是完全均匀的。

==Reservations==

==Reservations==