2014/03/30 by Jordan M. Horowitz, Takahiro Sagawa
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Entropy (arrow of time) #Entropy production #Generalized relative entropy #Joint quantum entropy #Kullback–Leibler divergence #Mathematical analysis #Mathematics #Monotonic function #Non-equilibrium thermodynamics #Open quantum system #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum operation #Quantum relative entropy #Quantum thermodynamics #Statistical physics #Thermal Radiation and Cooling Technologies #Von Neumann entropy #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1007/s10955-014-0991-1
published as J. Stat. Phys. 156, 55-65 (2014) · 13 pages
arxiv created 2014/03/30 · openalex publication_date 2014/04/21 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The nonadiabatic entropy production is a useful tool for the thermodynamic analysis of continuously dissipating, nonequilibrium steady states. For open quantum systems, two seemingly distinct definitions for the nonadiabatic entropy production have appeared in the literature, one based on the quantum relative entropy and the other based on quantum trajectories. We show that these two formulations are equivalent. Furthermore, this equivalence leads us to a proof of the monotonicity of the quantum relative entropy under a special class of completely-positive, trace-preserving quantum maps, which circumvents difficulties associated with the noncommuntative structure of operators.