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On the elementary information content of thermodynamic ensembles

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, $\mathcal{P}(β)$, and for phase-space projectors related to the quantum fidelity, $\mathcal{F}(β)$, are explicitly derived in terms of an explicit correspondence with the related partition function, $\mathcal{Z}(β)$. 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.