QSTAR & CNR-Istituto Nazionale di Ottica, Largo Enrico Fermi 2, I-50125 Firenze, Italy.
Phys Rev E. 2017 May;95(5-1):052135. doi: 10.1103/PhysRevE.95.052135. Epub 2017 May 22.
The notion of negative absolute temperature emerges naturally from Boltzmann's definition of "surface" microcanonical entropy in isolated systems with a bounded energy density. Recently, the well-posedness of such construct has been challenged, on account that only the Gibbs "volume" entropy-and the strictly positive temperature thereof-would give rise to a consistent thermodynamics. Here we present analytical and numerical evidence that Boltzmann microcanonical entropy provides a consistent thermometry for both signs of the temperature. In particular, we show that Boltzmann (negative) temperature allows the description of phase transitions occurring at high energy densities, at variance with Gibbs temperature. Our results apply to nonlinear lattice models standardly employed to describe the propagation of light in arrays of coupled wave guides and the dynamics of ultracold gases trapped in optical lattices. Optically induced photonic lattices, characterized by saturable nonlinearity, are particularly appealing because they offer the possibility of observing states and phase transitions at both signs of the temperature.
从玻尔兹曼对具有有限能量密度的孤立系统中“表面”微正则熵的定义中，自然会出现负绝对温度的概念。最近，由于只有吉布斯“体积”熵及其严格为正的温度才会产生一致的热力学，这种构造的适定性受到了挑战。在这里，我们提出了分析和数值证据，表明玻尔兹曼微正则熵为温度的两个符号提供了一致的测温法。特别地，我们表明，玻尔兹曼（负）温度允许描述在高能量密度下发生的相变，这与吉布斯温度不同。我们的结果适用于标准地用于描述在耦合波导阵列中光传播和被光学晶格捕获的超冷气体动力学的非线性晶格模型。具有可饱和非线性的光诱导光子晶格特别有吸引力，因为它们提供了在温度的两个符号上观察状态和相变的可能性。
