{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T23:46:30Z","timestamp":1771631190371,"version":"3.50.1"},"reference-count":14,"publisher":"AIP Publishing","issue":"23","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,12,21]]},"abstract":"<jats:p>We revisit a two-temperature Nos\u00e9\u2013Hoover wanderer particle embedded in a two-dimensional periodic 2 \u00d7 2 cell with four smooth repulsive corners at (x, y) = (\u00b11, \u00b11) to explore chaos with anisotropic thermostatting. The model employs separate thermostats in the x and y directions, enabling controlled deviations from equilibrium. By integrating the full six-dimensional equations of motion and computing the complete Lyapunov spectrum, we confirm chaos and quantify phase-space contraction from the fully resolved six-dimensional Lyapunov spectrum. The total contraction rate, interpreted as entropy production, increases nonlinearly with the thermostat anisotropy, deviating from the quadratic dependence expected from linear-response theory, \u039b \u221d \u03b42. We analyze two functional forms for the entropy-production rate, \u039b(\u03b4) (with \u03b4 = 0.5 \u2212 Ty): (i) a quadratic-plus-quartic expansion, consistent with linear-response expectations, and (ii) a power law, \u039b \u221d \u03b42.44. While the latter captures the low-driving regime slightly better, the former more accurately describes the strongly driven regime and remains consistent with linear-response theory near equilibrium. An empirical linear relation between dissipation and phase-space dimensionality loss is also identified, \u039b \u2248 (DKY \u2212 6)\/3, where DKY is the approximate Kaplan\u2013Yorke dimension. Momentum statistics show a significant non-Gaussian behavior under strong driving. Despite its dissipative nature, the model remains strictly time-reversible, offering a pedagogically rich example of microscopic reversibility coexisting with macroscopic entropy production.<\/jats:p>","DOI":"10.1063\/5.0307531","type":"journal-article","created":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T12:41:12Z","timestamp":1765802472000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Chaos in nonequilibrium two-temperature (\n                    <i>T<\/i>\n                    <i>x<\/i>\n                    ,\n                    <i>T<\/i>\n                    <i>y<\/i>\n                    ) Nos\u00e9\u2013Hoover cell models"],"prefix":"10.1063","volume":"163","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3198-5733","authenticated-orcid":false,"given":"Hesam","family":"Arabzadeh","sequence":"first","affiliation":[{"name":"Department of Chemistry, University of Missouri 1 , Columbia, Missouri 65211,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carol Griswold","family":"Hoover","sequence":"additional","affiliation":[{"name":"Ruby Valley Research Institute, Unit 109 2 , 2870 Ruby Vista Drive, Elko, Nevada 89801,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1717-052X","authenticated-orcid":false,"given":"William Graham","family":"Hoover","sequence":"additional","affiliation":[{"name":"Ruby Valley Research Institute, Unit 109 2 , 2870 Ruby Vista Drive, Elko, Nevada 89801,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-8993-5488","authenticated-orcid":false,"given":"Brad Lee","family":"Holian","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory 3 , Los Alamos, New Mexico 87545,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2025,12,15]]},"reference":[{"key":"2025121507410878500_c1","doi-asserted-by":"publisher","first-page":"1695","DOI":"10.1103\/physreva.31.1695","article-title":"Canonical dynamics: Equilibrium phase-space distributions","volume":"31","year":"1985","journal-title":"Phys. Rev. A"},{"key":"2025121507410878500_c2","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1080\/00268978400101201","article-title":"A molecular dynamics method for simulations in the canonical ensemble","volume":"52","year":"1984","journal-title":"Mol. Phys."},{"key":"2025121507410878500_c3","doi-asserted-by":"publisher","first-page":"17","DOI":"10.12921\/cmst.2024.0000005","article-title":"Canonical temperature control by molecular dynamics","volume":"30","year":"2024","journal-title":"Comput. Methods Sci. Technol."},{"key":"2025121507410878500_c4","volume-title":"Statistical Mechanics of Nonequilibrium Liquids","year":"2008"},{"key":"2025121507410878500_c5","doi-asserted-by":"publisher","first-page":"2635","DOI":"10.1063\/1.463940","article-title":"Nos\u00e9\u2013Hoover chains: The canonical ensemble via continuous dynamics","volume":"97","year":"1992","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025121507410878500_c6","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1063\/1.165860","article-title":"Heat transfer between two degrees of freedom","volume":"1","year":"1991","journal-title":"Chaos"},{"key":"2025121507410878500_c7","doi-asserted-by":"publisher","first-page":"977","DOI":"10.1103\/revmodphys.77.977","article-title":"Microfluidics: Fluid physics at the nanoliter scale","volume":"77","year":"2005","journal-title":"Rev. Mod. Phys."},{"key":"2025121507410878500_c8","doi-asserted-by":"publisher","first-page":"011305","DOI":"10.1063\/1.4832615","article-title":"Nanoscale thermal transport. II. 2003\u20132012","volume":"1","year":"2014","journal-title":"Appl. Phys. Rev."},{"key":"2025121507410878500_c9","doi-asserted-by":"publisher","first-page":"109","DOI":"10.12921\/cmst.2015.21.03.001","article-title":"Comparison of very smooth cell-model trajectories using five symplectic and two Runge\u2013Kutta integrators","volume":"21","year":"2015","journal-title":"Comput. Methods Sci. Technol."},{"key":"2025121507410878500_c10","doi-asserted-by":"publisher","first-page":"3616","DOI":"10.1103\/physrevlett.71.3616","article-title":"Probability of second law violations in shearing steady states","volume":"71","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"2025121507410878500_c11","doi-asserted-by":"publisher","first-page":"2338","DOI":"10.1103\/physreva.14.2338","article-title":"Kolmogorov entropy and numerical experiments","volume":"14","year":"1976","journal-title":"Phys. Rev. A"},{"key":"2025121507410878500_c12","doi-asserted-by":"publisher","first-page":"2175","DOI":"10.1103\/physreva.39.2175","article-title":"Equilibrium and nonequilibrium Lyapunov spectra for dense fluids and solids","volume":"39","year":"1989","journal-title":"Phys. Rev. A"},{"key":"2025121507410878500_c13","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s00440-023-01197-6","article-title":"Periodic Lorentz gas with small scatterers","volume":"186","year":"2023","journal-title":"Probab. Theory Relat. Fields"},{"key":"2025121507410878500_c14","doi-asserted-by":"publisher","first-page":"2338","DOI":"10.1103\/physreve.52.2338","article-title":"Thermostatted molecular dynamics: How to avoid the Toda demon hidden in Nos\u00e9\u2013Hoover dynamics","volume":"52","year":"1995","journal-title":"Phys. Rev. E"}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0307531\/20837366\/234104_1_5.0307531.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0307531\/20837366\/234104_1_5.0307531.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T12:41:13Z","timestamp":1765802473000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/163\/23\/234104\/3374756\/Chaos-in-nonequilibrium-two-temperature-Tx-Ty-Nose"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,15]]},"references-count":14,"journal-issue":{"issue":"23","published-print":{"date-parts":[[2025,12,21]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0307531","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,12,21]]},"published":{"date-parts":[[2025,12,15]]},"article-number":"234104"}}