Abstract We show that both positive and negative absolute temperatures and monotonically increasing and decreasing entropy in adiabatic processes are consistent with Caratheodory's version of the second law and we explore the modifications of the Kelvin–Planck and Clausius versions which are needed to accommodate these possibilities. We show, in part by using the equivalence of distributions and the canonical distribution, that the correct microcanonical entropy, is the surface (Boltzmann) form rather than the bulk (Gibbs) form thereby providing for the possibility of negative temperatures and we counter the contention on the part of a number of authors that the surface entropy fails to satisfy fundamental thermodynamic relationships.

中文翻译：

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热力学和统计力学中的负温度问题

摘要我们表明绝热过程中的正，负绝对温度以及熵的单调增加和减少与第二定律的Caratheodory版本是一致的，并且我们探索了Kelvin-Planck和Clausius版本的修改，以适应这些可能性。我们使用分布的等式和典范分布来证明，正确的微规范熵是表面（玻尔兹曼）形式而不是整体（吉布斯）形式，从而提供了出现负温度的可能性，并且我们对抗了争论一些作者认为表面熵不能满足基本的热力学关系。