A unifying picture of generalized thermodynamic uncertainty relations
| Autor: | Davide Gabrielli, Alessandra Faggionato, Andre C. Barato, Raphael Chetrite |
|---|---|
| Přispěvatelé: | Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Class (set theory) Current (mathematics) [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas Quadratic equation 0103 physical sciences thermodynamic uncertainty relations FOS: Mathematics Applied mathematics [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] 010306 general physics Linear combination Condensed Matter - Statistical Mechanics Mathematical Physics ComputingMilieux_MISCELLANEOUS Mathematics Statistical Mechanics (cond-mat.stat-mech) Markov chain Probability (math.PR) Statistical and Nonlinear Physics Mathematical Physics (math-ph) Thermodynamic system [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Flow (mathematics) Large deviations theory Statistics Probability and Uncertainty Mathematics - Probability |
| Zdroj: | Journal of Statistical Mechanics: Theory and Experiment Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2019, 2019 (8), pp.084017. ⟨10.1088/1742-5468/ab3457⟩ |
| ISSN: | 1742-5468 |
| DOI: | 10.1088/1742-5468/ab3457⟩ |
| Popis: | The thermodynamic uncertainty relation is a universal trade-off relation connecting the precision of a current with the average dissipation at large times. For continuous time Markov chains (also called Markov jump processes) this relation is valid in the time-homogeneous case, while it fails in the time-periodic case. The latter is relevant for the study of several small thermodynamic systems. We consider here a time-periodic Markov chain with continuous time and a broad class of functionals of stochastic trajectories, which are general linear combinations of the empirical flow and the empirical density. Inspired by the analysis done in our previous work [1], we provide general methods to get local quadratic bounds for large deviations, which lead to universal lower bounds on the ratio of the diffusion coefficient to the squared average value in terms of suitable universal rates, independent of the empirical functional. These bounds are called "generalized thermodynamic uncertainty relations" (GTUR's), being generalized versions of the thermodynamic uncertainty relation to the time-periodic case and to functionals which are more general than currents. Previously, GTUR's in the time-periodic case have been obtained in [1, 27, 42]. Here we recover the GTUR's in [1, 27] and produce new ones, leading to even stronger bounds and also to new trade-off relations for time-homogeneous systems. Moreover, we generalize to arbitrary protocols the GTUR obtained in [42] for time-symmetric protocols. We also generalize to the time-periodic case the GTUR obtained in [19] for the so called dynamical activity, and provide a new GTUR which, in the time-homogeneous case, is stronger than the one in [19]. The unifying picture is completed with a comprehensive comparison between the different GTUR's. Comment: 37 pages, 1 figure, 2 tables |
| Databáze: | OpenAIRE |
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