2016/09/30 by Álvaro M. Alhambra, Mischa P. Woods
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Bounded function #Detailed balance #Entropy (arrow of time) #Entropy production #Joint quantum entropy #Mathematical analysis #Mathematics #Open quantum system #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum mechanics #Quantum relative entropy #Statistical physics #Thermalisation #quant-ph
paper · pdf · doi:10.1103/physreva.96.022118
published as Phys. Rev. A 96, 022118 (2017) · main text: 5 pages. Appendix: 11 pages. V3: The conjectures in V2 have been proven. This is close to the journal published version, but with improved citations
openalex publication_date 2017/08/14 · arxiv created 2017/08/17 · arxiv updated 2017/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Markovian master equations (formally known as quantum dynamical semigroups) can be used to describe the evolution of a quantum state \ensuremathρ when in contact with a memoryless thermal bath. This approach has had much success in describing the dynamics of real-life open quantum systems in the laboratory. Such dynamics increase the entropy of the state \ensuremathρ and the bath until both systems reach thermal equilibrium, at which point entropy production stops. Our main result is to show that the entropy production at time t is bounded by the relative entropy between the original state and the state at time 2t. The bound puts strong constraints on how quickly a state can thermalize, and we prove that the factor of 2 is tight. The proof makes use of a key physically relevant property of these dynamical semigroups, detailed balance, showing that this property is intimately connected with the field of recovery maps from quantum information theory. We envisage that the connections made here between the two fields will have further applications. We also use this connection to show that a similar relation can be derived when the fixed point is not thermal.