{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:21:56Z","timestamp":1767705716090,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T00:00:00Z","timestamp":1652140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","award":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"],"award-info":[{"award-number":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"]}]},{"name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","award":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"],"award-info":[{"award-number":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"]}]},{"name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","award":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"],"award-info":[{"award-number":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"]}]},{"name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Pesquisa","award":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"],"award-info":[{"award-number":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"]}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"publisher","award":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"],"award-info":[{"award-number":["2018\/06365-4","2018\/21285-7","2020\/02170-4","141018\/2017-8","DMR-2010127"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>While quantum phase transitions share many characteristics with thermodynamic phase transitions, they are also markedly different as they occur at zero temperature. Hence, it is not immediately clear whether tools and frameworks that capture the properties of thermodynamic phase transitions also apply in the quantum case. Concerning the crossing of thermodynamic critical points and describing its non-equilibrium dynamics, the Kibble\u2013Zurek mechanism and linear response theory have been demonstrated to be among the very successful approaches. In the present work, we show that these two approaches are also consistent in the description of quantum phase transitions, and that linear response theory can even inform arguments of the Kibble\u2013Zurek mechanism. In particular, we show that the relaxation time provided by linear response theory gives a rigorous argument for why to identify the \u201cgap\u201d as a relaxation rate, and we verify that the excess work computed from linear response theory exhibits Kibble\u2013Zurek scaling.<\/jats:p>","DOI":"10.3390\/e24050666","type":"journal-article","created":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T08:31:55Z","timestamp":1652171515000},"page":"666","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Kibble\u2013Zurek Scaling from Linear Response Theory"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2684-9147","authenticated-orcid":false,"given":"Pierre","family":"Naz\u00e9","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica \u2018Gleb Wataghin\u2019, Universidade Estadual de Campinas, Campinas 13083-859, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7283-3034","authenticated-orcid":false,"given":"Marcus V. 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