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Article

Velocity Multistability vs. Ergodicity Breaking in a Biased Periodic Potential

1
Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
2
Institute of Physics, University of Augsburg, Universitätstr. 1, 86135 Augsburg, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Antonio Maria Scarfone
Entropy 2022, 24(1), 98; https://doi.org/10.3390/e24010098
Received: 16 December 2021 / Revised: 4 January 2022 / Accepted: 5 January 2022 / Published: 7 January 2022
Multistability, i.e., the coexistence of several attractors for a given set of system parameters, is one of the most important phenomena occurring in dynamical systems. We consider it in the velocity dynamics of a Brownian particle, driven by thermal fluctuations and moving in a biased periodic potential. In doing so, we focus on the impact of ergodicity—A concept which lies at the core of statistical mechanics. The latter implies that a single trajectory of the system is representative for the whole ensemble and, as a consequence, the initial conditions of the dynamics are fully forgotten. The ergodicity of the deterministic counterpart is strongly broken, and we discuss how the velocity multistability depends on the starting position and velocity of the particle. While for non-zero temperatures the ergodicity is, in principle, restored, in the low temperature regime the velocity dynamics is still affected by initial conditions due to weak ergodicity breaking. For moderate and high temperatures, the multistability is robust with respect to the choice of the starting position and velocity of the particle. View Full-Text
Keywords: multistability; ergodicity; Brownian motion; tilted periodic potential multistability; ergodicity; Brownian motion; tilted periodic potential
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MDPI and ACS Style

Spiechowicz, J.; Hänggi, P.; Łuczka, J. Velocity Multistability vs. Ergodicity Breaking in a Biased Periodic Potential. Entropy 2022, 24, 98. https://doi.org/10.3390/e24010098

AMA Style

Spiechowicz J, Hänggi P, Łuczka J. Velocity Multistability vs. Ergodicity Breaking in a Biased Periodic Potential. Entropy. 2022; 24(1):98. https://doi.org/10.3390/e24010098

Chicago/Turabian Style

Spiechowicz, Jakub, Peter Hänggi, and Jerzy Łuczka. 2022. "Velocity Multistability vs. Ergodicity Breaking in a Biased Periodic Potential" Entropy 24, no. 1: 98. https://doi.org/10.3390/e24010098

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