薛定谔-吉布斯系综中的非广延热力学函数
Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble
摘要：
薛定谔建议，量子函数不能基于量子力学能级（通常是哈密顿算符的正交本征态）是量子系统唯一允许的状态的无端指控[E。Schrödinger，Statistical Thermodynamics（C. Dover，Mineola，1967）]。不同的作者通过引入量子纯态空间上的密度分布来解释这一说法，其中权重是系统哈密顿量期望值的函数。在这项工作中，我们重点关注这些分布中最著名的分布之一，并且我们证明，当在复合量子系统中考虑时，它定义了不分解为非相互作用子系统的配分函数的乘积的配分函数，即使在热力学状态下也是如此。这意味着不可能通过使用这些模型来定义广泛的热力学量，例如自由能、内能或热力学熵。因此，我们得出结论，这种分布的灵感薛定谔的想法不能用来构建一个适当的量子平衡热力学。
英文摘要：
Schrödinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schrödinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions, and we prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schrödinger's idea can not be used to construct an appropriate quantum equilibrium thermodynamics.
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