Monteoliva D, Plastino A, Plastino A R
UNLP-Comisión de Investigaciones Científicas Provincia de Buenos Aires La Plata, La Plata 1900, Argentina.
Instituto de Física La Plata-CCT-CONICET, Universidad Nacional de La Plata, La Plata 1900, Argentina.
Entropy (Basel). 2023 Aug 14;25(8):1206. doi: 10.3390/e25081206.
We consider an fermion system at low temperature in which we encounter special particle number values Nm exhibiting special traits. These values arise when focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all -values but experience sudden jumps at the Nm. For a quantum state described by the matrix ρ, its purity is expressed by Trρ2 and then the degree of mixture is given by 1-Trρ2, a quantity that coincides with the entropy Sq for q=2. Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity. Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systems that are usually manipulated at zero temperature. Here, we wish to study the subject at finite temperature. The Gibbs ensemble is appealed to. Some interesting insights are thereby gained.
我们考虑一个处于低温的费米子系统，在其中我们会遇到呈现特殊特征的特殊粒子数取值Nm。当关注相关量子态的混合度（DM）时，这些取值就会出现。给定哈密顿量的耦合常数，对于所有取值，DM保持恒定，但在Nm处会经历突然跳跃。对于由矩阵ρ描述的量子态，其纯度由Trρ²表示，那么混合度由1 - Trρ²给出，这个量在q = 2时与熵Sq一致。因此，指数为2的Tsallis熵如实地代表了一个态的混合程度，也就是说，它衡量了该态偏离最大纯度的程度。混合度的宏观表现可以通过各种物理量来观察。我们目前的研究与通常在零温度下操控的多费米子系统的性质密切相关。在此，我们希望在有限温度下研究这个主题。我们诉诸吉布斯系综。由此获得了一些有趣的见解。
