2019/09/16 by Li Gao, Marius Junge, Nicholas LaRacuente · 1 citation
Mathematics · Neuroscience · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Conditional quantum entropy #Entropy (arrow of time) #Entropy rate #Generalized relative entropy #Joint quantum entropy #Kullback–Leibler divergence #Mathematics #Maximum entropy thermodynamics #Min entropy #Neural dynamics and brain function #Physics #Principle of maximum entropy #Pure mathematics #Quantum #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum relative entropy #Statistics #Von Neumann architecture #Von Neumann entropy #math.OA
paper · pdf · doi:10.1142/s0129167x20500469
published as International Journal of Mathematics, Vol. 31, No. 06, 2050046 (2020) · Minor changes. Added reference and examples; 32 pages. Comments are welcome!
arxiv created 2019/09/16 · openalex publication_date 2020/03/07 · arxiv updated 2020/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We revisit the connection between index and relative entropy for an inclusion of finite von Neumann algebras. We observe that the Pimsner–Popa index connects to sandwiched [Formula: see text]-Rényi relative entropy for all [Formula: see text], including Umegaki’s relative entropy at [Formula: see text]. Based on that, we introduce a new notation of relative entropy to a subalgebra which generalizes subfactors index. This relative entropy has application in estimating decoherence time of quantum Markov semigroups.