{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T12:06:13Z","timestamp":1769169973740,"version":"3.49.0"},"reference-count":63,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,25]],"date-time":"2023-12-25T00:00:00Z","timestamp":1703462400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development","doi-asserted-by":"publisher","award":["465618\/2014-6"],"award-info":[{"award-number":["465618\/2014-6"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development","doi-asserted-by":"publisher","award":["E-26\/202.529\/2019"],"award-info":[{"award-number":["E-26\/202.529\/2019"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004586","name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estadodo Rio de Janeiro","doi-asserted-by":"publisher","award":["465618\/2014-6"],"award-info":[{"award-number":["465618\/2014-6"]}],"id":[{"id":"10.13039\/501100004586","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004586","name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estadodo Rio de Janeiro","doi-asserted-by":"publisher","award":["E-26\/202.529\/2019"],"award-info":[{"award-number":["E-26\/202.529\/2019"]}],"id":[{"id":"10.13039\/501100004586","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size L is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, Th and Tl (Th&gt;Tl), respectively. These particles at the extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators (i=2,\u22ef,L\u22121) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier\u2019s law for the heat flux is verified numerically, with the thermal conductivity becoming independent of the lattice size in the limit L\u2192\u221e, scaling with the temperature, as \u03ba(T)\u223cT\u22122.25, where T=(Th+Tl)\/2. Moreover, the thermal conductance, \u03c3(L,T)\u2261\u03ba(T)\/L, is well-fitted by a function, which is typical of nonextensive statistical mechanics, according to \u03c3(L,T)=Aexpq(\u2212Bx\u03b7), where A and B are constants, x=L0.475T, q=2.28\u00b10.04, and \u03b7=2.88\u00b10.04.<\/jats:p>","DOI":"10.3390\/e26010025","type":"journal-article","created":{"date-parts":[[2023,12,25]],"date-time":"2023-12-25T22:59:09Z","timestamp":1703545149000},"page":"25","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["First-Principle Validation of Fourier\u2019s Law: One-Dimensional Classical Inertial Heisenberg Model"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3833-0190","authenticated-orcid":false,"given":"Henrique Santos","family":"Lima","sequence":"first","affiliation":[{"name":"Centro Brasileiro de Pesquisas F\u00edsicas, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil"},{"name":"National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9387-9194","authenticated-orcid":false,"given":"Constantino","family":"Tsallis","sequence":"additional","affiliation":[{"name":"Centro Brasileiro de Pesquisas F\u00edsicas, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil"},{"name":"National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil"},{"name":"Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA"},{"name":"Complexity Science Hub Vienna, Josefst\u00e4dter Strasse 39, 1080 Vienna, Austria"}]},{"given":"Fernando Dantas","family":"Nobre","sequence":"additional","affiliation":[{"name":"Centro Brasileiro de Pesquisas F\u00edsicas, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil"},{"name":"National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,25]]},"reference":[{"key":"ref_1","unstructured":"Fourier, J.B.J. 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