{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:14:08Z","timestamp":1760148848530,"version":"build-2065373602"},"reference-count":41,"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":"Ministero dell\u2019Universit\u00e0 e della Ricerca (Italy), grant Dipartimenti di Eccellenza 2018\u20132022","award":["E11G18000350001"],"award-info":[{"award-number":["E11G18000350001"]}]},{"name":"Italian National Group of Mathematical Physics (GNFM) of INdAM.","award":["E11G18000350001"],"award-info":[{"award-number":["E11G18000350001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We consider several Hamiltonian systems perturbed by external agents that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite reservoirs and from the onset of processes breaking the time-reversal symmetry. We analyze exactly solvable oscillator systems and perform simulations of relatively more complex ones. This indicates that the standard statistical mechanical formalism needs to be adjusted in the ever more investigated nano-scale science and technology. In particular, the hypothesis that heat reservoirs be considered infinite and be described by the classical ensembles is found to be critical when exponential quantities are considered since the large size limit may not coincide with the infinite size canonical result. Furthermore, process-dependent emergent irreversibility affects ensemble averages, effectively frustrating, on a statistical level, the time reversal invariance of Hamiltonian dynamics that are used to obtain numerous results.<\/jats:p>","DOI":"10.3390\/sym15061268","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T01:31:31Z","timestamp":1686879091000},"page":"1268","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Finite Reservoirs Corrections to Hamiltonian Systems Statistics and Time Symmetry Breaking"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7424-7888","authenticated-orcid":false,"given":"Matteo","family":"Colangeli","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica, Universit\u00e0 degli Studi dell\u2019Aquila, via Vetoio, 67100 L\u2019Aquila, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8108-6325","authenticated-orcid":false,"given":"Antonio","family":"Di Francesco","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria e Scienze dell\u2019Informazione e Matematica, Universit\u00e0 degli Studi dell\u2019Aquila, via Vetoio, 67100 L\u2019Aquila, 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":"Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 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":[[2023,6,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/0021-9991(76)90078-4","article-title":"Efficient estimation of free energy differences from Monte Carlo data","volume":"22","author":"Bennett","year":"1976","journal-title":"J. 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