{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:03:54Z","timestamp":1760238234513,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T00:00:00Z","timestamp":1596067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["Dipartimenti di Eccellenza 2018\u20132022"],"award-info":[{"award-number":["Dipartimenti di Eccellenza 2018\u20132022"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An exact response theory has recently been developed within the field of Nonequilibrium Molecular Dynamics. Its main ingredient is known as the Dissipation Function, \u03a9. This quantity determines nonequilbrium properties like thermodynamic potentials do with equilibrium states. In particular, \u03a9 can be used to determine the exact response of particle systems obeying classical mechanical laws, subjected to perturbations of arbitrary size. Under certain conditions, it can also be used to express the response of a single system, in contrast to the standard response theory, which concerns ensembles of identical systems. The dimensions of \u03a9 are those of a rate, hence \u03a9 can be associated with the entropy production rate, provided local thermodynamic equilibrium holds. When this is not the case for a particle system, or generic dynamical systems are considered, \u03a9 can equally be defined, and it yields formal, thermodynamic-like, relations. While such relations may have no physical content, they may still constitute interesting characterizations of the relevant dynamics. Moreover, such a formal approach turns physically relevant, because it allows a deeper analysis of \u03a9 and of response theory than possible in case of fully fledged physical models. Here, we investigate the relation between linear and exact response, pointing out conditions for the validity of the response theory, as well as difficulties and opportunities for the physical interpretation of certain formal results.<\/jats:p>","DOI":"10.3390\/e22080835","type":"journal-article","created":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T12:15:38Z","timestamp":1596111338000},"page":"835","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Dissipation Function: Nonequilibrium Physics and Dynamical Systems"],"prefix":"10.3390","volume":"22","author":[{"given":"Salvatore","family":"Caruso","sequence":"first","affiliation":[{"name":"Department of Physics, Informatics and Mathematics, Universit\u00e0 di Modena and Reggio Emilia, via G.Campi 213\/b, I-41125 Modena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5788-3903","authenticated-orcid":false,"given":"Claudio","family":"Giberti","sequence":"additional","affiliation":[{"name":"Department of Sciences and Methods for Engineering, Universit\u00e0 di Modena and Reggio Emilia, via G.Amendola 2, I-42122 Reggio Emilia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy"},{"name":"INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Fermi, E., Pasta, P., Ulam, S., and Tsingou, M. 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