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Article

Nonequilibrium Time Reversibility with Maps and Walks

1
Ruby Valley Research Institute, 601 Highway Contract 60, Ruby Valley, NV 89833, USA
2
Department of Mechanical and Aerospace Engineering, Brunel University London, Uxbridge UB8 3PH, UK
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Author to whom correspondence should be addressed.
Academic Editor: J. Gonzalo Muga
Entropy 2022, 24(1), 78; https://doi.org/10.3390/e24010078
Received: 22 October 2021 / Revised: 16 December 2021 / Accepted: 25 December 2021 / Published: 1 January 2022
Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt’s and Zermélo’s paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the irreversible Second Law of Thermodynamics (Loschmidt’s) as well as periodic in the time (Zermélo’s, illustrating Poincaré recurrence). Understanding these paradoxical aspects of time-reversible systems is enhanced here by studying the simplest pair of such model systems. The first is time-reversible, but nevertheless dissipative and periodic, the piecewise-linear compressible Baker Map. The fractal properties of that two-dimensional map are mirrored by an even simpler example, the one-dimensional random walk, confined to the unit interval. As a further puzzle the two models yield ambiguities in determining the fractals’ information dimensions. These puzzles, including the classical paradoxes, are reviewed and explored here. View Full-Text
Keywords: nonequilibrium simulations; time reversibility; fractals; baker maps; random walks nonequilibrium simulations; time reversibility; fractals; baker maps; random walks
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MDPI and ACS Style

Hoover, W.G.; Hoover, C.G.; Smith, E.R. Nonequilibrium Time Reversibility with Maps and Walks. Entropy 2022, 24, 78. https://doi.org/10.3390/e24010078

AMA Style

Hoover WG, Hoover CG, Smith ER. Nonequilibrium Time Reversibility with Maps and Walks. Entropy. 2022; 24(1):78. https://doi.org/10.3390/e24010078

Chicago/Turabian Style

Hoover, William G., Carol G. Hoover, and Edward R. Smith. 2022. "Nonequilibrium Time Reversibility with Maps and Walks" Entropy 24, no. 1: 78. https://doi.org/10.3390/e24010078

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