2025/10/08 by Andrzej Łuczak, Łuczak, Andrzej, Hanna Podsȩdkowska +3
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Control and Stability of Dynamical Systems #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2510.07605
openalex publication_date 2025/10/08 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
The paper presents variational formulae for entropy-like functionals, including Segal and Rényi entropies, for normal states on semifinite von Neumann algebras. The considered functionals are of the form τ(f(h)) where τ is a normal faithful semifinite trace on this algebra, h is a positive selfadjoint operator from L1(\M,τ), and f is an appropriate convex or concave function. The results cover both finite and semifinite algebras, and the obtained formulae generalise known results, in particular, those concerning relative entropy. Moreover, the connection between quantum entropies and the structure of abelian subalgebras is highlighted, providing new interpretations in the context of quantum information theory.