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Title: Nonequilibrium Time Reversibility with Maps and Walks
Authors: Hoover, WG
Hoover, CG
Smith, ER
Keywords: Nonequilibrium simulations;Time reversibility;Fractals;Baker maps;Random walks
Issue Date: 1-Jan-2022
Publisher: MDPI
Citation: Hoover, W.G.; Hoover, C.G.; Smith, E.R. Nonequilibrium Time Reversibility with Maps and Walks. Entropy 2022, 24, 78.
Abstract: 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.
ISSN: 1099-4300
Appears in Collections:Dept of Mechanical and Aerospace Engineering Research Papers

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