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……在从一个平衡态到另一个平衡态的不可逆或自发的变化中（例如，当两个物体 A 和 B 接触时的温度平衡过程），熵总是增加。
……在从一个平衡态到另一个平衡态的不可逆或自发的变化中（例如，当两个物体 A 和 B 接触时的温度平衡过程），熵总是增加。
===Principle of Carathéodory 卡拉西奥多里原理===
===Principle of Carathéodory 卡拉西奥多里原理===
Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as follows:
Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as follows:
'''康斯坦丁·卡拉西奥多里 Constantin Carathéodory'''在纯数学公理的基础上进行了热力学公理化。他对第二定律的陈述被称为'''卡拉西奥多里原理 Principle of Carathéodory'''，可以这样表述:
'''康斯坦丁·卡拉西奥多里 Constantin Carathéodory'''在纯数学公理的基础上进行了热力学<font color = 'red'><s>公理化</s></font><font color = 'blue'>阐明</font>。他对第二定律的陈述被称为'''卡拉西奥多里原理 Principle of Carathéodory'''，可以这样表述:
--[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|讨论]]） formulated 可以译为公理化（Axiomatic）吗？存疑
<blockquote>In every neighborhood of any state S of an adiabatically enclosed system there are states inaccessible from S.<ref>Buchdahl, H.A. (1966), p. 68.</ref></blockquote>
<blockquote>In every neighborhood of any state S of an adiabatically enclosed system there are states inaccessible from S.<ref>Buchdahl, H.A. (1966), p. 68.</ref></blockquote>
With this formulation, he described the concept of adiabatic accessibility for the first time and provided the foundation for a new subfield of classical thermodynamics, often called geometrical thermodynamics. It follows from Carathéodory's principle that quantity of energy quasi-statically transferred as heat is a holonomic process function, in other words, <math>\delta Q=TdS</math>.
With this formulation, he described the concept of adiabatic accessibility for the first time and provided the foundation for a new subfield of classical thermodynamics, often called geometrical thermodynamics. It follows from Carathéodory's principle that quantity of energy quasi-statically transferred as heat is a holonomic process function, in other words, <math>\delta Q=TdS</math>.
<font color = 'red'><s>公理化处理后，</s></font><font color = 'blue'>通过这个阐明，</font>他<font color = 'red'><s>第一次</s></font><font color = 'blue'>首次</font>描述了'''绝热可达性 Adiabatic Accessibility'''的概念，并成为经典热力学的一个新的子领域，即通常所说的'''几何热力学 Geometrical Thermodynamics'''<font color = 'red'><s>奠定了基础</s></font>。由卡拉西奥多里原理可以推出，<font color = 'red'><s>准静态转移的热量值是一个可积过程函数，</s></font><font color = 'blue'>作为热的能量的准静态转移是一个完整的过程函数</font>即<math>\delta Q=TdS</math>。
--[[用户:Dorr|Dorr]]（[[用户讨论:Dorr|讨论]]）准静态转移的热量值是一个可积过程函数 存疑
--[[用户:Dorr|Dorr]]（[[用户讨论:Dorr|讨论]]）准静态转移的热量值是一个可积过程函数 存疑
--[[用户:嘉树|嘉树]]（[[用户讨论:嘉树|讨论]]）本句的修改供讨论。可积函数的英文应该是Integrable function。但是什么是完整的函数存疑，是连续的函数？
Though it is almost customary in textbooks to say that Carathéodory's principle expresses the second law and to treat it as equivalent to the Clausius or to the Kelvin-Planck statements, such is not the case. To get all the content of the second law, Carathéodory's principle needs to be supplemented by Planck's principle, that isochoric work always increases the internal energy of a closed system that was initially in its own internal thermodynamic equilibrium.
Though it is almost customary in textbooks to say that Carathéodory's principle expresses the second law and to treat it as equivalent to the Clausius or to the Kelvin-Planck statements, such is not the case. To get all the content of the second law, Carathéodory's principle needs to be supplemented by Planck's principle, that isochoric work always increases the internal energy of a closed system that was initially in its own internal thermodynamic equilibrium.
尽管在教科书几乎惯称卡拉西奥多里原理<font color = 'red'><s>表述了第二定律</s></font><font color = 'blue'>也是第二定律的一种表述</font>，并认为其与克劳修斯表述或开尔文-普朗克表述等价，但事实并非如此。为了得到第二定律的所有内容，需要对卡拉西奥多里原理补充普朗克表述，即等量功总是增加一个最初处于自身内部热力学平衡的封闭系统的内部能量。
... there is only one way in which the entropy of a [closed] system can be decreased, and that is to transfer heat from the system.
... there is only one way in which the entropy of a [closed] system can be decreased, and that is to transfer heat from the system.
……只有一种方法可以减少<font color = 'red'><s>[闭合]</s></font><font color = 'blue'>（封闭）</font>系统的熵，那就是从系统中转移热量。
The second law has been shown to be equivalent to the internal energy U being a weakly convex function, when written as a function of extensive properties (mass, volume, entropy, ...).
The second law has been shown to be equivalent to the internal energy U being a weakly convex function, when written as a function of extensive properties (mass, volume, entropy, ...).
写成广泛性质（质量，体积，熵……）的函数时，第二定律被证明等价于弱凸函数内能 U。
--[[用户:Dorr|Dorr]]（[[用户讨论:Dorr|讨论]]）存疑
--[[用户:Dorr|Dorr]]（[[用户讨论:Dorr|讨论]]）存疑