负温度：进一步延伸
Negative temperature: further extensions
摘要：
本文是在M. Baldovin，S.尤比尼河Livi和A. Vulpiani，负温度系统的统计力学，arXiv：2103.12572。作者认为负的绝对温度与平衡热力学是一致的。这是正确的，如果环境也有负温度。否则，这些状态代表短暂的，虽然可能是长期存在的亚稳态效应。这里我们考虑负温度到相对论系统的推广。我们证明了负态在Dirac真空中是可能的，这是由传统的Dirac海通过$PT$对称变换得到的。如果这种粒子数相反的真空充满了整个宇宙，那么由负温度决定的热力学就达到了平衡。
英文摘要：
This paper is motivated by the recent paper M. Baldovin, S. Iubini, R. Livi and A. Vulpiani, Statistical mechanics of systems with negative temperature, arXiv:2103.12572. The authors suggest that negative absolute temperatures are consistent with equilibrium thermodynamics. This is correct, if the environment also has negative temperature. Otherwise such states represent the transient though maybe long-lived metastable effects. Here we consider the extension of the negative temperatures to the relativistic systems. We show that the negative state is possible in the Dirac vacuum, which is obtained by the $PT$ symmetry transformation from the conventional Dirac sea. If such vacuum with inverse population fills the whole Universe, its thermodynamics determined by negative temperatures becomes equilibrium.
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