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→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。
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">强度 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">强度 Intensive</font>'''参数在整个系统中是均匀的，而局部热力学平衡(LTE)意味着这些强度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强度参数的变化过大，那么这些强度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，粒子需要一定数量的碰撞来平衡其周围环境。如果在这些碰撞中移动的平均距离使它离开平衡邻域，它将永远不会平衡，也就不会有 LTE。根据定义，温度与平衡邻域的平均内部能量成正比。由于没有达到平衡邻域，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 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'''<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。
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，或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.
例如，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.
局部热力学平衡不需要局部或全局的平稳性。换句话说，每一个小区域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缓慢到足以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，通过在水杯中不断添加细粉冰来补偿熔化，并持续排出融水，可以保持全球稳定的静止状态。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。回顾我们的例子，热量的扩散将导致我们的玻璃杯水流向全局热力学平衡，在这种状态下，玻璃杯的温度是完全均匀的。
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