Alonso J L, Castro A, Clemente-Gallardo J, Cuchí J C, Echenique P, Esteve J G, Falceto F
Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain.
Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, Mariano Esquillor s/n, 50018 Zaragoza, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Feb;91(2):022137. doi: 10.1103/PhysRevE.91.022137. Epub 2015 Feb 25.
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 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 cannot be used to construct an appropriate quantum equilibrium thermodynamics.
薛定谔认为，热力学函数不能基于这样一个无端的假设，即量子力学能级（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[E.薛定谔，《统计热力学》（信使多佛出版社，米尼奥拉，1967年）]。不同的作者通过在量子纯态空间上引入密度分布来解释这一说法，其权重是作为系统哈密顿量期望值的函数获得的。在这项工作中，我们关注这些分布中最著名的一种，并证明，当在复合量子系统中考虑时，它所定义的配分函数即使在热力学极限下也不会分解为非相互作用子系统配分函数的乘积。这意味着不可能通过使用这些模型来定义诸如自由能、内能或热力学熵等广延热力学量。因此，我们得出结论，这种受薛定谔思想启发的分布不能用于构建合适的量子平衡热力学。
