{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:45:20Z","timestamp":1760143520141,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,11]],"date-time":"2024-02-11T00:00:00Z","timestamp":1707609600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"publisher","award":["12247106","11975189","P2022Z7ZAJ","CUP: E53D23018070001"],"award-info":[{"award-number":["12247106","11975189","P2022Z7ZAJ","CUP: E53D23018070001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Italian Ministry of University and Research (MUR)","award":["12247106","11975189","P2022Z7ZAJ","CUP: E53D23018070001"],"award-info":[{"award-number":["12247106","11975189","P2022Z7ZAJ","CUP: E53D23018070001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The fluctuation relation stands as a fundamental result in nonequilibrium statistical physics. Its derivation, particularly in the stationary state, places stringent conditions on the physical systems of interest. On the other hand, numerical analyses usually do not directly reveal any specific connection with such physical properties. This study proposes an investigation of such a connection with the fundamental ingredients of the derivation of the fluctuation relation for the dissipation, which includes the decay of correlations, in the case of heat transport in one-dimensional systems. The role of the heat baths in connection with the system\u2019s inherent properties is then highlighted. A crucial discovery of our research is that different lattice models obeying the steady-state fluctuation relation may do so through fundamentally different mechanisms, characterizing their intrinsic nature. Systems with normal heat conduction, such as the lattice \u03d54 model, comply with the theorem after surpassing a certain observational time window, irrespective of lattice size. In contrast, systems characterized by anomalous heat conduction, such as Fermi\u2013Pasta\u2013Ulam\u2013Tsingou-\u03b2 and harmonic oscillator chains, require extended observation periods for theoretical alignment, particularly as the lattice size increases. In these systems, the heat bath\u2019s fluctuations significantly influence the entire lattice, linking the system\u2019s fluctuations with those of the bath. Here, the current autocorrelation function allows us to discern the varying conditions under which different systems satisfy with the fluctuation relation. Our findings significantly expand the understanding of the stationary fluctuation relation and its broader implications in the field of nonequilibrium phenomena.<\/jats:p>","DOI":"10.3390\/e26020156","type":"journal-article","created":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T03:50:27Z","timestamp":1707709827000},"page":"156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fluctuation Relation for the Dissipative Flux: The Role of Dynamics, Correlations and Heat Baths"],"prefix":"10.3390","volume":"26","author":[{"given":"Xubin","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Physics, Xiamen University, Xiamen 361005, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4223-6279","authenticated-orcid":false,"given":"Lamberto","family":"Rondoni","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Politecnico di Torino, 10129 Turin, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, 10125 Turin, Italy"}]},{"given":"Hong","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Physics, Xiamen University, Xiamen 361005, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2401","DOI":"10.1103\/PhysRevLett.71.2401","article-title":"Probability of second law violations in shearing steady states","volume":"71","author":"Evans","year":"1993","journal-title":"Phys. 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