Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics over almost one century and a half exhibit positive absolute temperature, because their entropy is a nondecreasing function of energy. Since more than half a century ago it has been realized that this may not be the case for some physical systems as incompressible fluids, nuclear magnetic chains, lasers, cold atoms and optical waveguides. We review these examples and discuss their peculiar thermodynamic properties, which have been associated to the presence of thermodynamic regimes, characterized by negative absolute temperatures. As reported in this review, the ambiguity inherent the definition of entropy has recurrently raised a harsh debate about the possibility of considering negative temperature states as genuine thermodynamic equilibrium ones. Here we show that negative absolute temperatures are consistent with equilibrium as well as with non-equilibrium thermodynamics. In particular, thermometry, thermodynamics of cyclic transformations, ensemble equivalence, fluctuation–dissipation relations, response theory and even transport processes can be reformulated to include them, thus dissipating any prejudice about their exceptionality, typically presumed as a manifestation of transient metastable effects.

负绝对温度与物理学特别是统计物理学有关系吗？我们提供的证据表明，我们可以肯定地对这个vexata quaestio做出积极的回答。由统计力学研究的绝大多数模型在近一个半世纪中表现出正的绝对温度，因为它们的熵是能量的不变函数。自半个多世纪以来，人们已经意识到，对于某些物理系统，例如不可压缩的流体，核磁链，激光器，冷原子和光波导，可能并非如此。我们回顾了这些例子并讨论了它们独特的热力学性质，这些性质与以负绝对温度为特征的热力学状态的存在有关。正如这篇评论中所报道的那样，熵的定义固有的含混性经常引起关于将负温度状态视为真正的热力学平衡状态的可能性的激烈争论。在这里，我们显示负的绝对温度与平衡以及非平衡热力学一致。特别是，可以重新构造测温法，循环变换的热力学，集合等价，波动-耗散关系，响应理论甚至传输过程，以包括它们，从而消除了对它们特殊性的任何偏见，通常被认为是瞬态亚稳态效应的表现。