{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:36:27Z","timestamp":1760142987794,"version":"build-2065373602"},"reference-count":60,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,20]],"date-time":"2024-01-20T00:00:00Z","timestamp":1705708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Italian Ministry of University and Research (MUR)","award":["P2022Z7ZAJ","E53D23018070001"],"award-info":[{"award-number":["P2022Z7ZAJ","E53D23018070001"]}]},{"name":"Italian National Group of Mathematical Physics (GNFM) of the Istituto Nazionale di Alta Matematica (INdAM)","award":["P2022Z7ZAJ","E53D23018070001"],"award-info":[{"award-number":["P2022Z7ZAJ","E53D23018070001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We show how averages of exponential functions of path-dependent quantities, such as those of Work Fluctuation Theorems, detect phase transitions in deterministic and stochastic systems. State space truncation\u2014the restriction of the observations to a subset of state space with prescribed probability\u2014is introduced to obtain that result. Two stochastic processes undergoing first-order phase transitions are analyzed both analytically and numerically: a variant of the Ehrenfest urn model and the 2D Ising model subject to a magnetic field. In the presence of phase transitions, we prove that even minimal state space truncation makes averages of exponentials of path-dependent variables sensibly deviate from full state space values. Specifically, in the case of discontinuous phase transitions, this approach is strikingly effective in locating the transition value of the control parameter. As this approach works even with variables different from those of fluctuation theorems, it provides a new recipe to identify order parameters in the study of non-equilibrium phase transitions, profiting from the often incomplete statistics that are available.<\/jats:p>","DOI":"10.3390\/sym16010125","type":"journal-article","created":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T03:50:22Z","timestamp":1705895422000},"page":"125","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Detecting Phase Transitions through Non-Equilibrium Work Fluctuations"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7424-7888","authenticated-orcid":false,"given":"Matteo","family":"Colangeli","sequence":"first","affiliation":[{"name":"Department of Information Engineering, Computer Science and Mathematics, University of L\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":"Department of Information Engineering, Computer Science and Mathematics, University of L\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":"Department of Mathematical Sciences \u201cGiuseppe Luigi Lagrange\u201d, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy"},{"name":"National Institute for Nuclear Physics, Sezione di Torino, Via Pietro Giuria 1, 10125 Turin, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,20]]},"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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