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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'''<font color = '#ff8000'>绝热可达性 Adiabatic Accessibility</font>'''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'''<font color = '#ff8000'>几何热力学  Geometrical Thermodynamics</font>'''<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>准静态转移的热的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'''<font color="#ff8000"> 完整的过程函数</font>'''</font>即<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'''<font color = '#ff8000'>绝热可达性 Adiabatic Accessibility</font>'''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'''<font color = '#ff8000'>几何热力学  Geometrical Thermodynamics</font>'''<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>准静态转移的热的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'''<font color="#ff8000"> 完整的过程函数holonomic process function</font>'''</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