2021/04/26 by Paolo Facchi, Giovanni Gramegna, Arturo Konderak
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Conditional quantum entropy #Density matrix #Entropy (arrow of time) #Generalized relative entropy #Joint quantum entropy #Observable #Operator algebra #Quantum Information and Cryptography #Quantum many-body systems #Quantum relative entropy #Von Neumann algebra #Von Neumann entropy #math-ph #math.MP #quant-ph
paper · pdf · doi:10.3390/e23060645
published as Entropy 23 (2021) 645 · 20 pages, 2 figures
arxiv created 2021/04/26 · openalex created_date 2021/05/10 · openalex publication_date 2021/05/21 · arxiv updated 2021/05/25 · openalex updated_date 2026/08/05
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.