Brownian motion surviving in the unstable cubic potential and the role of Maxwell's demon

Physical Review. E
Luca OrnigottiRadim Filip

Abstract

The trajectories of an overdamped particle in a highly unstable potential diverge so rapidly, that the variance of position grows much faster than its mean. A description of the dynamics by moments is therefore not informative. Instead, we propose and analyze local directly measurable characteristics, which overcome this limitation. We discuss the most probable particle position (position of the maximum of the probability density) and the local uncertainty in an unstable cubic potential, V(x)∼x^{3}, both in the transient regime and in the long-time limit. The maximum shifts against the acting force as a function of time and temperature. Simultaneously, the local uncertainty does not increase faster than the observable shift. In the long-time limit, the probability density naturally attains a quasistationary form. We interpret this process as a stabilization via the measurement-feedback mechanism, the Maxwell demon, which works as an entropy pump. The rules for measurement and feedback naturally arise from the basic properties of the unstable dynamics. All reported effects are inherent in any unstable system. Their detailed understanding will stimulate the development of stochastic engines and amplifiers and, later, their quantu...Continue Reading

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Citations

Apr 20, 2019·Physical Review. E·Viktor HolubecStefano Steffenoni
Apr 24, 2019·Physical Review Letters·Erez AghionEli Barkai
May 20, 2020·Physical Review. E·Jonas StapmannsMoritz Helias
Dec 24, 2018·Physical Review Letters·Martin ŠilerRadim Filip
Feb 20, 2020·Physical Review. E·Igor PetrovićMiroljub Dugić
Oct 6, 2020·Physical Review Letters·Gianmaria Falasco, Massimiliano Esposito
Nov 21, 2020·Physical Review. E·Alexander A DubkovDavide Valenti
Jan 1, 2021·Chaos·Karol CapałaBartłomiej Dybiec

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