{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/nonequilibrium-time-reversibility-with-maps","title":"Nonequilibrium Time Reversibility with Maps and Walks","arxiv_id":"2108.02251","date":"2021-08-04","proceeding":null,"authors":["William Graham Hoover","Carol Griswold Hoover","Edward R. Smith"],"abstract":"Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt's and Zerm\\'elo's paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the {\\it irreversible} Second Law of Thermodynamics (Loschmidt's) as well as {\\it periodic} in the time (Zerm\\'elo's, illustrating Poincar\\'e 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. We review our investigations presented in Budapest in 1997 and end with presentday questions posed as the Snook Prize Problems in 2020 and 2021.","url_abs":"https://arxiv.org/abs/2108.02251v3","url_pdf":"https://arxiv.org/pdf/2108.02251v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"nonequilibrium-time-reversibility-with-maps","repo_url":"https://github.com/edwardsmith999/fractal_phase_space","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}