{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T01:48:45Z","timestamp":1777081725225,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T00:00:00Z","timestamp":1686787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)","award":["UIDB\/04434\/2020"],"award-info":[{"award-number":["UIDB\/04434\/2020"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)","award":["UIDP\/04434\/2020"],"award-info":[{"award-number":["UIDP\/04434\/2020"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)","award":["CERN\/FIS-PAR\/0037\/2019"],"award-info":[{"award-number":["CERN\/FIS-PAR\/0037\/2019"]}]},{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)","award":["PTDC\/FIS-AST\/0054\/2021"],"award-info":[{"award-number":["PTDC\/FIS-AST\/0054\/2021"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work, we explore the formalism of the irreversible thermodynamics of open systems and the possibility of gravitationally generated particle production in modified gravity. More specifically, we consider the scalar\u2013tensor representation of f(R,T) gravity, in which the matter energy\u2013momentum tensor is not conserved due to a nonminimal curvature\u2013matter coupling. In the context of the irreversible thermodynamics of open systems, this non-conservation of the energy\u2013momentum tensor can be interpreted as an irreversible flow of energy from the gravitational sector to the matter sector, which, in general, could result in particle creation. We obtain and discuss the expressions for the particle creation rate, the creation pressure, and the entropy and temperature evolutions. Applied together with the modified field equations of scalar\u2013tensor f(R,T) gravity, the thermodynamics of open systems lead to a generalization of the \u039bCDM cosmological paradigm, in which the particle creation rate and pressure are considered effectively as components of the cosmological fluid energy\u2013momentum tensor. Thus, generally, modified theories of gravity in which these two quantities do not vanish provide a macroscopic phenomenological description of particle production in the cosmological fluid filling the Universe and also lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy.<\/jats:p>","DOI":"10.3390\/e25060944","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T02:54:33Z","timestamp":1686884073000},"page":"944","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Irreversible Geometrothermodynamics of Open Systems in Modified Gravity"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1327-0996","authenticated-orcid":false,"given":"Miguel A. S.","family":"Pinto","sequence":"first","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Faculdade de Ci\u00eancias da Universidade de Lisboa, Campo Grande, Edif\u00edcio C8, 1749-016 Lisbon, Portugal"},{"name":"Departamento de F\u00edsica, Faculdade de Ci\u00eancias da Universidade de Lisboa, Campo Grande, Edif\u00edcio C8, 1749-016 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1990-9172","authenticated-orcid":false,"given":"Tiberiu","family":"Harko","sequence":"additional","affiliation":[{"name":"Department of Physics, Babes-Bolyai University, Kogalniceanu Street, 400084 Cluj-Napoca, Romania"},{"name":"Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering (IFIN-HH), 077125 Bucharest, Romania"},{"name":"Astronomical Observatory, 19 Ciresilor Street, 400487 Cluj-Napoca, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9388-8373","authenticated-orcid":false,"given":"Francisco S. N.","family":"Lobo","sequence":"additional","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Faculdade de Ci\u00eancias da Universidade de Lisboa, Campo Grande, Edif\u00edcio C8, 1749-016 Lisbon, Portugal"},{"name":"Departamento de F\u00edsica, Faculdade de Ci\u00eancias da Universidade de Lisboa, Campo Grande, Edif\u00edcio C8, 1749-016 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7428","DOI":"10.1073\/pnas.85.20.7428","article-title":"Thermodynamics of cosmological matter creation","volume":"85","author":"Prigogine","year":"1988","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1007\/BF00758981","article-title":"Thermodynamics and cosmology","volume":"21","author":"Prigogine","year":"1989","journal-title":"Gen. Relativ. 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