Contributors: Institut de Mathématiques de Toulouse UMR5219 (IMT); Université Toulouse Capitole (UT Capitole); Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse); Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J); Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3); Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Analyse, Géométrie et Modélisation (AGM - UMR 8088); Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY); CY Cergy Paris Université (CY); Department of Mathematics and Statistics McGill University; McGill University = Université McGill Montréal, Canada; Centre de Physique Théorique - UMR 7332 (CPT); Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS); Université de Toulon (UTLN); CPT - E8 Dynamique quantique et analyse spectrale; Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS); CPT - E5 Physique statistique et systèmes complexes; NSERC; FRQNT-CRM-CNRS; CRM Simons; ANR-20-CE40-0024,QTraj,Trajectoires quantiques(2020); ANR-16-IDEX-0008,PSI,PSI(2016); ANR-20-CE47-0014,ESQuisses,Évolutions Stochastiques Quantiques(2020)
نبذة مختصرة : International audience ; Recent theoretical investigations of the two-times measurement entropy production (2TMEP) in quantum statistical mechanics have shed a new light on the mathematics and physics of the quantum-mechanical probabilistic rules. Among notable developments are the extensions of entropic fluctuation relations to quantum domain and discovery of a deep link between 2TMEP and modular theory of operator algebras. All these developments concerned the setting where the state of the system at the instant of the first measurement is the same as the state whose entropy production is measured. In this work we consider the case where these two states are different and link this more general 2TEMP to modular theory. The established connection allows us to show that under general ergodicity assumptions the 2TEMP is essentially independent of the choice of the system state at the instant of the first measurement due to a decoherence effect induced by the first measurement. This stability sheds a new light on the concept of quantum entropy production, and, in particular, on possible quantum formulations of the celebrated classical Gallavotti--Cohen Fluctuation Theorem which will be studied in the continuation of this work.
Processing Request
No Comments.