On the elementary information content of thermodynamic ensembles

TL;DR

This paper develops a framework linking thermodynamic ensembles' quantum information content to their spectral properties and partition functions, enhancing understanding of quantum thermodynamics.

Contribution

It introduces explicit formulas for quantum purity and fidelity in thermodynamic ensembles, connecting them to the partition function and extending quantum thermodynamics analysis.

Findings

Derived expressions for quantum purity and fidelity in thermal states.

Established a correspondence between phase-space projectors and the partition function.

Extended the role of the partition function in quantum thermodynamics.

Abstract

Extending the definition of phase-space (Wigner) quantum projectors to thermodynamic ensembles usually results into an efficient platform for quantifying their elementary information content. Given the spectral decomposition profile of a thermalized quantum system, general expressions for the quantum purity quantifier, $\mathcal{P}(\beta)$, and for phase-space projectors related to the quantum fidelity, $\mathcal{F}(\beta)$, are explicitly derived in terms of an explicit correspondence with the related partition function, $\mathcal{Z}(\beta)$. Besides quantifying the storage of information capacity of thermodynamical ensembles, the tools here introduced extend the role of the partition function in expressing the quantum behavior of thermodynamic ensembles.