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The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.

The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are in contact then reach respective contact equilibria with one another.

If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.

If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.

如果几个系统彼此之间没有绝热壁，但是它们与世界其他部分共同隔离，那么它们就会达到多重接触平衡状态，并且它们有一个共同的温度，一个共同的内能，和一个共同的熵。在众多的变量中，这是温度的一个独特性质。即使在远距离作用力存在的情况下，它也是有效的。(也就是说，没有“力”可以维持温度的差异。)举个例子，在热力学平衡的一个垂直的引力场系统中，顶部壁面的压力比底部壁面的压力小，但是各处的温度都是一样的。

如果几个系统彼此之间没有绝热壁，但是它们与世界其他部分共同隔离，那么它们就会达到多重接触平衡状态，且有共同的温度，内能，和熵。在众多的变量中，这是温度的一个独特性质。即使在远距离作用力存在的情况下，它也是有效的。(也就是说，没有“力”可以维持温度的差异。)举个例子，在热力学平衡的一个垂直的引力场系统中，顶部壁面的压力比底部壁面的压力小，但是各处的温度都是一样的。

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'''<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。

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，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被放置或拆除。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Planck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>'''。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，由于初始状态和最终状态都是热力学平衡的，这在平衡热力学中也是允许的。一个自然过程在其主要过程中以有限的速率进行。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种，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。

通常可以很方便地假设周围的某些子系统比系统大得多，以至于这个过程只能影响周围子系统的密集变量，然后将这些子系统称为相关密集变量的储备库。

通常可以很方便地假设周围的某些子系统比系统大得多，以至于这个过程只能影响周围子系统的密集变量，然后将这些子系统称为相关密集变量的储备库。

== Local and global equilibrium ==

== Local and global equilibrium ==