2009/07/11 by Gian Paolo Beretta · 3 citations
Engineering · Physics and Astronomy · #Adiabatic process #Advanced Thermodynamics and Statistical Mechanics #Entropy (arrow of time) #Entropy production #Non-equilibrium thermodynamics #Nonlinear system #Quantum #Quantum many-body systems #Relaxation (psychology) #Second law of thermodynamics #Thermoelastic and Magnetoelastic Phenomena #quant-ph
paper · pdf · doi:10.1016/s0034-4877(09)90024-6
published as Reports on Mathematical Physics, Vol. 64, 139-168 (2009) · To appear in Reports on Mathematical Physics. Presented at the The Jubilee 40th Symposium on Mathematical Physics, "Geometry & Quanta", Torun, Poland, June 25-28, 2008
arxiv created 2009/07/11 · openalex publication_date 2009/08/01 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum theory of irreversibility and thermodynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors. The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any non-equilibrium density operator. It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics. We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems. This hinges on novel nonlinear projections defining local operators that we interpret as ``local perceptions'' of the overall system's energy and entropy. Each component particle contributes an independent local tendency along the direction of steepest increase of the locally perceived entropy at constant locally perceived energy. It conserves both the locally-perceived energies and the overall energy, and meets strong separability and non-signaling conditions, even though the local evolutions are not independent of existing correlations. We finally show how the geometrical construction can readily lead to other thermodynamically relevant models, such as of the nonunitary isoentropic evolution needed for full extraction of a system's adiabatic availability.