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Article

Entropy of Quantum States

1
Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari, Italy
2
Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Italy
3
Dipartimento di Fisica, Università di Trieste, I-34151 Trieste, Italy
*
Author to whom correspondence should be addressed.
Academic Editor: Rosario Lo Franco
Entropy 2021, 23(6), 645; https://doi.org/10.3390/e23060645
Received: 26 April 2021 / Revised: 15 May 2021 / Accepted: 18 May 2021 / Published: 21 May 2021
(This article belongs to the Special Issue Quantum Information and Quantum Optics)
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a minimality property of the von Neumann entropy of a density matrix with respect to its possible decompositions into pure states, we give a purely algebraic definition of entropy for states of an algebra of observables, thus solving the above ambiguity. The entropy so-defined satisfies all the desirable thermodynamic properties and reduces to the von Neumann entropy in the quantum mechanical case. Moreover, it can be shown to be equal to the von Neumann entropy of the unique representative density matrix belonging to the operator algebra of a multiplicity-free Hilbert-space representation. View Full-Text
Keywords: quantum entropy; operator algebra; quantum statistical mechanics quantum entropy; operator algebra; quantum statistical mechanics
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MDPI and ACS Style

Facchi, P.; Gramegna, G.; Konderak, A. Entropy of Quantum States. Entropy 2021, 23, 645. https://doi.org/10.3390/e23060645

AMA Style

Facchi P, Gramegna G, Konderak A. Entropy of Quantum States. Entropy. 2021; 23(6):645. https://doi.org/10.3390/e23060645

Chicago/Turabian Style

Facchi, Paolo, Giovanni Gramegna, and Arturo Konderak. 2021. "Entropy of Quantum States" Entropy 23, no. 6: 645. https://doi.org/10.3390/e23060645

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