Mapping of uncertainty relations between continuous and discrete time

Physical Review. E
Davide Chiuchiù, Simone Pigolotti

Abstract

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

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Citations

Sep 11, 2019·Physical Review. E·Tan Van Vu, Yoshihiko Hasegawa
May 19, 2018·Physical Review Letters·Alexandre P Solon, Jordan M Horowitz
Jul 25, 2019·Physical Review. E·Junjie Liu, Dvira Segal
Apr 12, 2019·Nature Communications·Junang LiNikta Fakhri
Jan 23, 2020·Physical Review. E·Daniel Maria Busiello, Simone Pigolotti
Oct 13, 2018·Physical Review Letters·Katarzyna MacieszczakJuan P Garrahan
Nov 28, 2019·Physical Review. E·Édgar Roldán, Pierpaolo Vivo
Dec 2, 2020·Physical Review Letters·David H Wolpert
Feb 20, 2021·Physical Review. E·Antoine Rignon-BretMark T Mitchison

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