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By using exact numerical and approximate analytical methods, we evaluate the free energy of this system at arbitrary interaction strengths and discuss strong-coupling modifications of derivative quantities such as the specific heat or the electric susceptibility. From this analysis we identify the lowest-order cavity-induced corrections to those quantities in the collective ultrastrong coupling regime and show that for even stronger interactions the presence of a single cavity mode can strongly modify extensive thermodynamic quantities of a large ensemble of dipoles. In this non-perturbative coupling regime we also observe a significant shift of the ferroelectric phase transition temperature and a characteristic broadening and collapse of the black-body spectrum of the cavity mode. Apart from a purely fundamental interest, these general insights will be important for identifying potential applications of ultrastrong-coupling effects, for example, in the field of quantum chemistry or for realizing quantum thermal machines.<\/jats:p>","DOI":"10.22331\/q-2020-09-28-335","type":"journal-article","created":{"date-parts":[[2020,9,28]],"date-time":"2020-09-28T12:45:26Z","timestamp":1601297126000},"page":"335","source":"Crossref","is-referenced-by-count":49,"title":["Thermodynamics of ultrastrongly coupled light-matter systems"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9935-3716","authenticated-orcid":false,"given":"Philipp","family":"Pilar","sequence":"first","affiliation":[{"name":"Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1040 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniele","family":"De Bernardis","sequence":"additional","affiliation":[{"name":"Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1040 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2560-8835","authenticated-orcid":false,"given":"Peter","family":"Rabl","sequence":"additional","affiliation":[{"name":"Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1040 Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2020,9,28]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"C. 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