{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T15:36:02Z","timestamp":1775057762742,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T00:00:00Z","timestamp":1715904000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Council of Finland","award":["312057"],"award-info":[{"award-number":["312057"]}]},{"name":"Research Council of Finland","award":["349601"],"award-info":[{"award-number":["349601"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We discuss the concept and realization of a heat bath in solid state quantum systems. We demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing, commonly considered as a reservoir of a quantum circuit, does not strictly qualify as a Caldeira\u2013Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We show that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance, in the form of superconducting resonators.<\/jats:p>","DOI":"10.3390\/e26050429","type":"journal-article","created":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T04:26:29Z","timestamp":1715919989000},"page":"429","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Heat Bath in a Quantum Circuit"],"prefix":"10.3390","volume":"26","author":[{"given":"Jukka P.","family":"Pekola","sequence":"first","affiliation":[{"name":"Pico Group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4752-4277","authenticated-orcid":false,"given":"Bayan","family":"Karimi","sequence":"additional","affiliation":[{"name":"Pico Group, QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland"},{"name":"QTF Centre of Excellence, Department of Physics, Faculty of Science, University of Helsinki, FI-00014 Helsinki, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"112001","DOI":"10.1088\/1361-6455\/aabcdf","article-title":"Thermalization and prethermalization in isolated quantum systems: A theoretical overview","volume":"51","author":"Mori","year":"2018","journal-title":"J. Phys. B At. Mol. Opt. 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