Lieb Elliott H, Yngvason Jakob
Department of Mathematics , Princeton University , Princeton, NJ 08542, USA ; Department of Physics , Princeton University , Princeton, NJ 08542, USA.
Proc Math Phys Eng Sci. 2013 Oct 8;469(2158):20130408. doi: 10.1098/rspa.2013.0408.
In earlier work, we presented a foundation for the second law of classical thermodynamics in terms of the entropy principle. More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all equilibrium states of all systems that has the appropriate additivity and scaling properties, and whose increase is a necessary and sufficient condition for an adiabatic process between two states to be possible. Here, after a brief review of this approach, we address the question of defining entropy for non-equilibrium states. Our conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties. We do show, however, that one can define two entropy functions, called and , which, taken together, delimit the range of adiabatic processes that can occur between non-equilibrium states. The concept of of states with respect to adiabatic changes plays an important role in our reasoning.
在早期的工作中，我们依据熵原理为经典热力学第二定律奠定了基础。更确切地说，我们给出了一个熵函数的基于经验可及的公理推导，该熵函数定义在所有系统的所有平衡态上，具有适当的可加性和标度性质，并且其增加是两个状态之间绝热过程能够发生的充要条件。在此，在对这种方法进行简要回顾之后，我们探讨为非平衡态定义熵的问题。我们的结论是，通常不可能找到一个具有所有相关物理性质的唯一熵。然而，我们确实表明，可以定义两个熵函数，称为(\varPhi)和(\varPsi)，它们共同界定了非平衡态之间可能发生的绝热过程的范围。关于绝热变化的态的(\varPhi)概念在我们的推理中起着重要作用。
