更改

根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊，因为在非平衡状态下发生冻结是非常普遍的。”

根据'''<font color="#ff8000">L.缇莎 L.Tisza</font>'''的说法: “ ... 在讨论接近绝对零度的现象时。经典理论的绝对预测变得特别模糊，因为在非平衡状态下发生冻结是非常普遍的。”

==Definitions==

==Definitions 定义==

 

The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.

The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.

一个系统最普遍的热力学平衡是通过与周围环境的接触，允许所有化学物质和各种能量同时通过。热力学平衡中的系统以均匀加速度在空间中运动，但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中，由远远大于系统本身的外部因素决定，因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的，并且确定了它的均匀加速度，或者它处于一个非均匀力场中，但是由于表面的局部力，例如机械压力，使它保持静止时，这个系统才能处于热力学平衡。

一个系统最普遍的热力学平衡是通过与周围环境的接触，允许所有化学物质和各种能量同时通过。热力学平衡中的系统可能以均匀加速度在空间中运动，但此时不能改变其形状或大小; 因此它是由空间中的刚性体积来定义的。它可能存在于外力场中，由远远大于系统本身的外部因素决定，因此系统内的事件不会对外力场产生相当大的影响。只有当外力场是均匀的，并且确定了它的均匀加速度，或者它处于一个非均匀力场中，但是由于表面的局部力，例如机械压力，使它保持静止时，这个系统才能处于热力学平衡。

For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.

For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.

例如，A. Münster写道：“当系统中没有以可测量的速度发生状态变化时，隔离系统处于热力学平衡状态。”这里有两项保留：系统是孤立的；任何状态的变化都是不可估量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明，讨论了第二个条件。Münster指出，热力学平衡状态所描述的宏观变量比给定系统任何其他状态都少。这是部分，但不完全是，因为系统内和系统内的所有流都是零。

例如，A. Münster写道：“当一个孤立系统中没有以可测量的速率发生状态变化时，系统处于热力学平衡状态。”这里有两项保留：系统是孤立的；任何状态的变化都是不可测量的缓慢。他通过对在室温且没有催化剂的情况下混合氧和氢的说明，讨论了第二个条件。Münster指出，描述热力学平衡状态所需要的宏观变量比给定系统任何其他状态都少。这是部分，但不完全是，因为系统内和流过系统的所有流都是零。

In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".

In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".

在一个标题为“热力学平衡”的章节中，H.B. Callen在段落定义了平衡状态.他指出，它们“是由系统内部的内在因素决定的”。它们是“终端状态” ，随着时间的推移，系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确，对于热力学平衡系统必须是孤立的;；Callen也没有说明他所说的“内在因素”是什么意思。

在一个标题为“热力学平衡”的章节中，H.B. Callen在一个段落中定义了平衡状态.他指出，它们“是由系统内部的内在因素决定的”。它们是“终端状态” ，随着时间的推移，系统会以“冰川般缓慢”的速度朝着这个终端状态演化。这个说法并没有明确，对于热力学平衡系统必须是孤立的;；Callen也没有说明他所说的“内在因素”是什么意思。

Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.

Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.

另一位教科书作者，C.J.Adkins，明确允许热力学平衡在非孤立的系统中发生。然而，他的系统在物质转移方面是封闭的。他写道: “一般来说，热力学平衡的方法包括热和类似变动与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。

另一位教科书作者，C.J.Adkins，明确允许热力学平衡在非孤立的系统中发生。然而，他的系统在物质转移方面是封闭的。他写道: “一般来说，热力学平衡的方法包括热和类似功的形式与周围环境的相互作用。”他将这种热力学平衡与只有通过热接触才能进行能量传递的热平衡相区别。

Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.

Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.

另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是，在提到“只是明显处于平衡状态”的系统时，他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样，Partington也指的是氧和氢的混合物。他补充说：“在一个真正的平衡状态，任何影响状态的外部条件的最小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。

另一位教科书作者'''<font color="#ff8000">J.R.帕廷顿 J.R.Partington</font>'''写道: “(i)平衡状态是独立于时间的状态。”但是，在提到“只是明显处于平衡状态”的系统时，他补充说: “这样的系统处于‘虚假平衡’状态。帕廷顿的陈述没有明确指出平衡是指一个孤立的系统。和Münster一样，Partington也指的是氧和氢的混合物。他补充说：“在一个真正的平衡状态，任何影响状态的外部条件的微小变化都会产生一个微小的状态变化... ... ”这个条件意味着热力学平衡必须在小的扰动下保持稳定; 这个要求对于热力学平衡的严格意义是必不可少的。

A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.

A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.

H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡，而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态，那么它将被称为处于平衡状态。”出于热力学描述的目的，Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说，只要实验测试表明‘慢’跃迁实际上是可逆的，玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分，而是假定相反的情况：如果热力学平衡中的一个体受到足够慢的过程的影响，则该过程可被视为足够接近可逆，并且该物体在过程中足够接近热力学平衡。

H.A. Buchdahl的一本关于经典热力学的专著考虑了热力学系统的平衡，而实际上并没有写热力学平衡一词。Buchdahl在提到封闭的物质交换系统时写道: “如果一个系统处于一个适当的静态状态，那么它将被称为处于平衡状态。”出于热力学描述的目的，Buchdahl的专著也讨论了非晶态玻璃。它说: “更准确地说，只要实验测试表明‘慢’跃迁实际上是可逆的，玻璃就可以被认为处于平衡状态。”通常来说不会将这一条件作为热力学平衡定义的一部分，而是假定相反的情况：如果热力学平衡中的一个物体受到足够慢的过程的影响，则该过程可被视为足够接近可逆，并且该物体在过程中足够接近热力学平衡。

A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions."  

A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions."  

通过引入接触平衡的概念，A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程，并特别关心开放系统，这些开放系统可能从周围环境获得或丢失物质。利益系统和周围系统之间的接触平衡，通过一种特殊的壁与利益系统接触，其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过，其他作家也提到过。它们具有选择渗透性。它们可能只对机械工作有渗透性，或者只对热有渗透性，或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如，只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分，都可以存在接触平衡。在接触平衡中，尽管有可能通过选择性渗透壁进行交换，感兴趣的系统是不变的，好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”

通过引入接触平衡的概念，A. Münster仔细地扩展了孤立系统热力学平衡的定义。这指定了在考虑非孤立系统的热力学平衡时允许的特定过程，并特别关心开放系统，这些开放系统可能从周围环境获得或丢失物质。感兴趣的系统和周围系统之间的接触平衡，通过一种特殊的壁与之接触，其余的连接系统是孤立的。这种特殊类型的壁也被'''<font color="#ff8000">C.喀喇西奥多里 C.Carathéodory</font>'''考虑过，其他作家也提到过。它们具有选择渗透性。它们可能只对机械功有渗透性，或者只对热有渗透性，或者只对某种特定的化学物质有渗透性。每个接触平衡定义了一个强度参数; 例如，只能透热的壁定义了一个经验温度。对于感兴趣的体系中每一种化学成分，都可以存在接触平衡。在接触平衡中，尽管有可能通过选择性渗透壁进行交换，但是感兴趣的系统是不变的，好像它处在孤立的热力学平衡。这个方案遵循的一般规则是: “ ... ... 我们只能考虑特定过程和特定实验条件下的平衡。”

[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref>

[[Mark Zemansky|M. Zemansky]] also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".<ref>[[Mark Zemansky|Zemansky, M.]] (1937/1968), p. 27.</ref>

'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了机械、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时，系统就处于热力学平衡状态。”

'''<font color="#ff8000">M.泽曼斯基 M.Zemansky</font>'''还区分了力学、化学和热平衡。他接着写道: “当这三种均衡的条件都满足时，系统就处于热力学平衡状态。”

P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.

P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.

Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref>

Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, ''thermodynamic equilibrium'' is said to exist." He is not here considering the presence of an external force field.<ref>Bailyn, M. (1994), p. 21.</ref>

考虑到平衡状态，M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、机械平衡和物质平衡。因此，他写道: “如果所有的强度变量都是一致的，那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。

考虑到平衡状态，M.Bailyn写道: “每个强度变量都有自己的平衡类型。”然后他定义了热平衡、力学平衡和物质平衡。因此，他写道: “如果所有的强度变量都是一致的，那么热力学平衡就是存在的。”他在这里没有考虑外力场的存在。

[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref>

[[John Gamble Kirkwood|J.G. Kirkwood]] and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of ''thermodynamic equilibrium'' if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.<ref>Kirkwood, J.G., Oppenheim, I. (1961), p. 2</ref>

'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态，如果，在分配给实验的时间内，(a)它强度特性与时间无关，(b)它的内部或与周围环境的边界处没有物质或能量流。”显然，他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性，并且超出了分配给实验的时间范围。他们注意到，对于两个相接触的系统，存在一个强度性质的小子类，如果这个小子类的所有子类都相等，那么所有各自的强度性质都相等。只要满足其他一些条件，热力学平衡状态可以由这个子类定义。

'''<font color="#ff8000">J.G.柯克伍德 J.G.Kirkwood</font>'''和 I.Oppenheim 将热力学平衡定义为: “一个系统处于热力学平衡状态，如果，在实验的时间内，(a)它强度特性与时间无关，(b)它的内部或与周围环境的边界处没有物质或能量流。”显然，他们没有把定义限制在孤立的或封闭的系统。它们不讨论“缓慢”发生变化的可能性，并且超出了分配给实验的时间范围。他们注意到，对于两个相接触的系统，存在一个强度性质的小子类，如果这个小子类的所有子类都相等，那么所有各自的强度性质都相等。只要满足其他一些条件，热力学平衡状态可以由这个子类定义。

==Characteristics of a state of internal thermodynamic equilibrium==

==Characteristics of a state of internal thermodynamic equilibrium==