{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,20]],"date-time":"2026-09-20T17:33:51Z","timestamp":1789925631111,"version":"4.0.1"},"reference-count":82,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,3,23]],"date-time":"2017-03-23T00:00:00Z","timestamp":1490227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","doi-asserted-by":"publisher","award":["17-06716S"],"award-info":[{"award-number":["17-06716S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The stochastic model of the Feynman\u2013Smoluchowski ratchet is proposed and solved using generalization of the Fick\u2013Jacobs theory. The theory fully captures nonlinear response of the ratchet to the difference of heat bath temperatures. The ratchet performance is discussed using the mean velocity, the average heat flow between the two heat reservoirs and the figure of merit, which quantifies energetic cost for attaining a certain mean velocity. Limits of the theory are tested comparing its predictions to numerics. We also demonstrate connection between the ratchet effect emerging in the model and rotations of the probability current and explain direction of the mean velocity using simple discrete analogue of the model.<\/jats:p>","DOI":"10.3390\/e19040119","type":"journal-article","created":{"date-parts":[[2017,3,23]],"date-time":"2017-03-23T06:40:37Z","timestamp":1490251237000},"page":"119","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Thermal Ratchet Effect in Confining Geometries"],"prefix":"10.3390","volume":"19","author":[{"given":"Viktor","family":"Holubec","sequence":"first","affiliation":[{"name":"Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holesovickach 2, 18000 Praha, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8593-9516","authenticated-orcid":false,"given":"Artem","family":"Ryabov","sequence":"additional","affiliation":[{"name":"Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holesovickach 2, 18000 Praha, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad","family":"Yaghoubi","sequence":"additional","affiliation":[{"name":"Complexity Science Group, Department of Physics &amp; Astronomy, University of Calgary, Calgary, AB T2N 1N4, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Varga","sequence":"additional","affiliation":[{"name":"Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holesovickach 2, 18000 Praha, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ayub","family":"Khodaee","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Zanjan, 45196-311 Zanjan, Iran"},{"name":"Bradley Plasma Lab, Department of Physics &amp; Engineering Physics, University of Saskatchewan, Saskatchewan, SK S7N 5E2, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Foulaadvand","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Zanjan, 45196-311 Zanjan, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Petr","family":"Chvosta","sequence":"additional","affiliation":[{"name":"Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holesovickach 2, 18000 Praha, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jacobs, M.H. 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