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平衡热力学 (查看源代码)

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~~{{short description|State of thermodynamic system(s) where no net macroscopic flow of matter or energy occurs}}~~

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'''Thermodynamic equilibrium''' is an [[axiomatic]] concept of [[thermodynamics]]. It is an internal [[State variables|state]] of a single [[thermodynamic system]], or a relation between several thermodynamic systems connected by more or less permeable or impermeable [[Thermodynamic system#Walls|walls]]. In thermodynamic equilibrium there are no net [[macroscopic]] [[Flow (mathematics)|flows]] of [[matter]] or of [[energy]], either within a system or between systems.

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Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems.

'''热力学平衡'''是'''热力学 Thermodynamics'''的一个'''不言自明的 Axiomatic'''概念。它是单个'''热力学系统 Thermodynamic System'''的内部'''状态 State'''，或者是几个热力学系统之间通过或多或少的渗透或不渗透的'''壁 Wall'''连接的关系。无论是在一个系统内还是在系统之间，在热力学平衡中不存在'''物质 Matter'''或'''能量 Energy'''的净'''宏观 Macroscopic''' '''流动 Flow'''。

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~~In a system that is in its own state of internal thermodynamic equilibrium, no [[macroscopic]] change occurs.~~

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~~In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs.~~

在一个处于内部热力学平衡状态的系统中，不会发生'''宏观 Macroscopic'''变化。

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Systems in mutual thermodynamic equilibrium are simultaneously in mutual [[Thermal equilibrium|thermal]], [[Mechanical equilibrium|mechanical]], [[Chemical equilibrium|chemical]], and [[Radiative equilibrium|radiative]] equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a [[thermodynamic operation]]. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.

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Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.

相互热力学平衡的体系同时处于互相之间的'''热 Thermal'''平衡、'''力学 Mechanical'''平衡、'''化学 Chemical'''平衡和'''辐射 Radiative'''平衡。系统可以处于其中一种相互平衡状态，尽管其他状态未平衡。在热力学平衡中所有的平衡同时并且无限期地保持，直到被'''热力学操作 Thermodynamic Operation'''打破。在一个宏观平衡中，微观交换是完全或几乎完全平衡的；这是对宏观平衡概念的物理解释。

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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform [[temperature]]. Its [[Intensive and extensive properties|intensive properties]], other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.

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A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.

一个处于内部热力学状态平衡的热力学系统具有空间均匀的'''温度 Temperature'''。除了温度以外，它的'''强度性质 Intensive Properties'''可以由于周围环境施加的不变的长程力场而导致空间不均匀性。

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In systems that are at a state of [[non-equilibrium]] there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a '''meta-stable equilibrium'''.

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In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.

相比之下，处于'''非平衡状态 non-equilibrium'''的系统中有物质或能量的净流动。如果这些变化可以在一个还没有发生的系统中被触发，那么这个系统就被称为处于一个'''亚稳定的平衡状态'''。

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Though not a widely named a "law," it is an [[axiom]] of thermodynamics that there exist states of thermodynamic equilibrium. The [[second law of thermodynamics]] states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the [[entropy|entropies]] of the portions.

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Though not a widely named a "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.

虽然不是一个广泛命名的“定律” ，但存在热力学平衡状态是一个热力学'''公理 Axiom'''。'''热力学第二定律 second law of thermodynamics'''指出，当一个物质体从一个平衡状态开始，在这个状态中，它的一部分被或多或少渗透或不渗透的分区保持在不同的状态，并且是孤立的，热力学操作移除分区或使分区更具渗透性，然后它会自发地达到自己内部热力学平衡的新状态，并伴随着部分'''熵 Entropy'''的总和增加。

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== ~~Overview~~ 概览==

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==概览==

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~~{{Thermodynamics|cTopic=[[Thermodynamic system|Systems]]}}~~

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Classical thermodynamics deals with states of [[dynamic equilibrium]]. The state of a system at thermodynamic equilibrium is the one for which some [[thermodynamic potential]] is minimized, or for which the [[entropy]] (''S'') is maximized, for specified conditions. One such potential is the [[Helmholtz free energy]] (''A''), for a system with surroundings at controlled constant temperature and volume:

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Classical thermodynamics deals with states of dynamic equilibrium. The state of a system at thermodynamic equilibrium is the one for which some thermodynamic potential is minimized, or for which the entropy (S) is maximized, for specified conditions. One such potential is the Helmholtz free energy (A), for a system with surroundings at controlled constant temperature and volume:

经典热力学研究'''动态平衡 Dynamic Equilibrium'''的状态。系统的热力学平衡状态是对于特定的条件，一些'''热力学势 Thermodynamic Potential'''被最小化，或者'''熵 Entropy'''(S)被最大化。对于一个周围环境温度和体积恒定的系统，其中一个这样的热力学势是'''亥姆霍兹自由能 Helmholtz Free Energy'''(A):

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~~:<math>A = U - TS</math>~~

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~~A = U-TS~~

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~~Another potential, the [[Gibbs free energy]] (''G''), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:~~

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~~Another potential, the Gibbs free energy (G), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:~~

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在恒定温度和压力的系统中，另一个热力学势'''吉布斯自由能 Gibbs Free Energy'''(G)在热力学平衡状态最小：

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在恒定温度和压力的系统中，另一个热力学势'''吉布斯自由能 Gibbs Free Energy'''<math>(G)</math>在热力学平衡状态最小：

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~~:<math>G = U - TS + PV</math>~~

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~~<math>G = U - TS + PV</math>~~

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其中<math>T</math> 表示热力学绝对温度，<math>P</math> 表示压强，<math>S</math> 表示熵，<math>V</math> 表示体积，<math>U</math> 表示体系的内能。

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~~where ''T'' denotes the absolute thermodynamic temperature, ''P'' the pressure, ''S'' the entropy, ''V'' the volume, and ''U'' the internal energy of the system.~~

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~~where T denotes the absolute thermodynamic temperature, P the pressure, S the entropy, V the volume, and U the internal energy of the system.~~

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~~其中 T 表示热力学绝对温度，P 表示压强，S 表示熵，V 表示体积，U 表示体系的内能。~~

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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.

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Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the particular conditions in the specified surroundings.

热力学平衡是一种独特的稳定定态，当系统长时间与周围环境相互作用时，它可以被接近或最终到达。上述势能是数学构造的热力学量，在特定的环境条件下最小化。

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== ~~Conditions~~ 条件==

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== 条件==

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* For a completely isolated system, ''S'' is maximum at thermodynamic equilibrium. 对于一个完全孤立的系统，S在热力学平衡中取最大值。

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* For a system with controlled constant temperature and volume, ''A'' is minimum at thermodynamic equilibrium. 对于一个恒定温度和体积的系统来说，A在热力学平衡中取最小值。

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* ~~For a system with controlled constant temperature and pressure, ''G'' is minimum at thermodynamic equilibrium. 对于一个恒温恒压的系统，G在热力学平衡中取最小值。~~

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* 对于一个完全孤立的系统，<math>S</math>在热力学平衡中取最大值。

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* 对于一个恒定温度和体积的系统来说，<math>A</math>在热力学平衡中取最小值。

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* 对于一个恒温恒压的系统，<math>G</math>在热力学平衡中取最小值。

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~~The various types of equilibriums are achieved as follows:~~

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~~The various types of equilibriums are achieved as follows:~~

实现各种类型的平衡的方法如下:

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*~~Two systems are in ''thermal equilibrium'' when their [[temperature]]s are the same.~~ 当两个系统的'''温度 Temperature'''相同时，它们就处于''热平衡状态''

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*当两个系统的'''温度 Temperature'''相同时，它们就处于''热平衡状态''。

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*Two systems are in ''mechanical equilibrium'' when their [[pressure]]s are the same. 当两个体系的'''压力 Pressure'''相同时，它们就处于''力学平衡''

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*Two systems are in ''diffusive equilibrium'' when their [[chemical potential]]s are the same. 当两个题体系的'''化学势 Chemical Potential'''相同时，它们就处于''扩散平衡''

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*All [[forces]] are balanced and there is no significant external driving force.

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~~所有的'''力 Force'''都是平衡的，没有明显的外部驱动力~~

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~~==Relation of exchange equilibrium between systems 系统之间的交换均衡关系==~~

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*当两个体系的'''压力 Pressure'''相同时，它们就处于''力学平衡''。

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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability.<~~ref name~~="~~Nster_a~~">~~Münster, A. (1970), p. 49.~~</~~ref~~> When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.

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*当两个题体系的'''化学势 Chemical Potential'''相同时，它们就处于''扩散平衡''。

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Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.

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*所有的'''力 Force'''都是平衡的，没有明显的外部驱动力。

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通常，热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中，我们可以把系统及其周围环境看作是相互接触的两个系统，远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中，该表面被认为具有特定的渗透性质。例如，接触的表面可能被认为只能透热，使能量只能作为热传递。当远程力在时间上不发生变化，两个系统之间的热量传递减慢并最终永久停止时，这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义。当两个系统对于某一特定类型的渗透率处于接触平衡时，它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。

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==系统之间的交换均衡关系==

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通常，热力学系统的周围环境也可以被看作是另一个热力学系统。在这种观点中，我们可以把系统及其周围环境看作是相互接触的两个系统，远程作用力也将它们联系在一起。系统的包围物是两个系统之间的接触面或边界。在热力学形式中，该表面被认为具有特定的渗透性质。例如，接触的表面可能被认为只能透热，使能量只能作为热传递。当远程力在时间上不发生变化，两个系统之间的热量传递减慢并最终永久停止时，这两个系统被称为热平衡; 这就是接触平衡的一个例子。其它类型的接触平衡可用其它类型的比渗透率来定义<ref name="Nster_a">Münster, A. (1970), p. 49.</ref> 。当两个系统对于某一特定类型的渗透率处于接触平衡时，它们具有属于该特定类型渗透率的强变量的共同值。这种强度变量的例子有温度、压力、化学势。

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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.

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A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.

接触平衡也可视为交换平衡。在接触平衡状态下，两系统之间某些量的传递速率存在零平衡。例如，对于只能透热的壁，内能作为热在两个系统之间的扩散速率是相等并反向的。两个系统之间的绝热壁只对作为功传递的能量有渗透作用; 在力学平衡，两个系统之间作为功的能量传递速率相等且相反。如果是一个简单的壁，那么通过它的体积转移率也是相等且相反的; 即它两边的压力是相等的。如果绝热壁比较复杂，有一种杠杆，有一个面积比，那么两个体系在交换平衡中的压力与体积交换比成反比，这使得转移率的零平衡作功。

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辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时，辐射交换平衡占优势。<ref name="Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref>

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~~A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.<ref name~~=~~"Planck 1914 40">[[Max Planck|Planck. M.]] (1914), p. 40.</ref>~~

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==系统内部平衡的热力学状态==

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~~A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.~~

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~~辐射交换可以发生在两个不同的系统之间。当两个体系温度相同时，辐射交换平衡占优势。~~

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物质的集合可能与其周围的环境完全'''孤立 Isolated'''。如果它在无限长的时间内一直保持不受干扰，按照经典热力学假定，它处于一个没有发生任何变化，没有流动的状态，即内部平衡的热力学状态。<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref>(这种假设有时被称为“负第一”热力学定律，但并不常见<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref>。有教科书称之为“第零定律” <ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> ，作者'''福勒 Fowler'''认为这个名称是'''更符合惯例的定义 More Customary Definition'''。)

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~~==Thermodynamic state of internal equilibrium of a system 系统内部平衡的热力学状态==~~

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A collection of matter may be entirely [[Isolated system|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.<ref>Haase, R. (1971), p. 4.</ref><ref>Callen, H.B. (1960/1985), p. 26.</ref> (This postulate is sometimes, but not often, called the "minus first" law of thermodynamics.<ref>{{Cite journal |doi = 10.1119/1.4914528|bibcode = 2015AmJPh..83..628M|title = Time and irreversibility in axiomatic thermodynamics|year = 2015|last1 = Marsland|first1 = Robert|last2 = Brown|first2 = Harvey R.|last3 = Valente|first3 = Giovanni|journal = American Journal of Physics|volume = 83|issue = 7|pages = 628–634}}</ref> One textbook<ref>[[George Uhlenbeck|Uhlenbeck, G.E.]], Ford, G.W. (1963), p. 5.</ref> calls it the "zeroth law", remarking that the authors think this more befitting that title than its [[Zeroth law of thermodynamics|more customary definition]], which apparently was suggested by [[Ralph H. Fowler|Fowler]].)

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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.)

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物质的集合可能与其周围的环境完全'''孤立 Isolated'''。如果它在无限长的时间内一直保持不受干扰，按照经典热力学假定，它处于一个没有发生任何变化，没有流动的状态，即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。有教科书称之为“第零定律” ，作者'''福勒 Fowler'''认为这个名称是'''更符合惯例的定义 More Customary Definition'''。)

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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.

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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.

这种状态是所谓的经典热力学或平衡态热力学的主要关注点，因为它们是系统中被认为在这门学科中得到很好定义的唯一状态。一个与另一个系统处于接触平衡状态可以被一个'''热力学操作 Thermodynamic Operation'''隔离，在隔离发生时，其内部不会发生任何变化。因此，一个与另一个系统处于接触平衡状态时也可以被视为处于其自身的内部热力学平衡状态。

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==~~Multiple contact equilibrium~~ 多点接触平衡==

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==多点接触平衡==

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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.

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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.

热力学形式允许一个系统同时与其他多个系统接触，这些系统可能有也可能没有相互接触，且这些接触具有不同的渗透性。如果这些系统都与世界其他部分相互隔离，那么它们彼此之间就会达到各自的接触平衡。

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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，总的内能和熵<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> 。在众多强度量中，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。

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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.<ref name="Caratheodory">Carathéodory, C. (1909).</ref><ref>Prigogine, I. (1947), p. 48.</ref><ref>Landsberg, P. T. (1961), pp. 128–142.</ref><ref>Tisza, L. (1966), p. 108.</ref> 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.

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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.

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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，总的内能和熵。在众多强度量中，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。

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