{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:48:14Z","timestamp":1760143694375,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T00:00:00Z","timestamp":1708992000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Sciences and Engineering Research Council of Canada","award":["#RGPIN-2020-07118","#RGPIN-2019-04183","#PJT-156317"],"award-info":[{"award-number":["#RGPIN-2020-07118","#RGPIN-2019-04183","#PJT-156317"]}]},{"name":"Canadian Institutes of Health Research","award":["#RGPIN-2020-07118","#RGPIN-2019-04183","#PJT-156317"],"award-info":[{"award-number":["#RGPIN-2020-07118","#RGPIN-2019-04183","#PJT-156317"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We present a modified version of the Szilard engine, demonstrating that an explicit measurement procedure is entirely unnecessary for its operation. By considering our modified engine, we are able to provide a new interpretation of Landauer\u2019s original argument for the cost of erasure. From this view, we demonstrate that a reset operation is strictly impossible in a dynamical system with only conservative forces. Then, we prove that approaching a reset yields an unavoidable instability at the reset point. Finally, we present an original proof of Landauer\u2019s principle that is completely independent from the Second Law of thermodynamics.<\/jats:p>","DOI":"10.3390\/e26030203","type":"journal-article","created":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T05:20:32Z","timestamp":1709011232000},"page":"203","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Precise Link between Energy and Information"],"prefix":"10.3390","volume":"26","author":[{"given":"Cameron","family":"Witkowski","sequence":"first","affiliation":[{"name":"Edward S. Rogers, Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 King\u2019s College Circle, Toronto, ON M5S 3G4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen","family":"Brown","sequence":"additional","affiliation":[{"name":"Edward S. Rogers, Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 King\u2019s College Circle, Toronto, ON M5S 3G4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kevin","family":"Truong","sequence":"additional","affiliation":[{"name":"Edward S. Rogers, Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 King\u2019s College Circle, Toronto, ON M5S 3G4, Canada"},{"name":"Institute of Biomedical Engineering, University of Toronto, 164 College Street, Toronto, ON M5S 3G9, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,27]]},"reference":[{"key":"ref_1","unstructured":"Knott, C.G. (1911). Life and Scientific Work of Peter Guthrie Tait, Cambridge University Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1002\/bs.3830090402","article-title":"On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings","volume":"9","author":"Szilard","year":"1964","journal-title":"Behav. 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Mathematical Methods of Classical Mechanics, Springer Science & Business Media."},{"key":"ref_7","unstructured":"Coddington, E.A., and Levinson, N. (1955). Theory of Ordinary Differential Equations, McGraw-Hill Book Company, Inc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/S1355-2198(98)00023-9","article-title":"EXORCIST XIV: The wrath of Maxwell\u2019s demon. Part I. From Maxwell to Szilard","volume":"Volume 29","author":"Earman","year":"1998","journal-title":"Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S1355-2198(98)00026-4","article-title":"EXORCIST XIV: The wrath of Maxwell\u2019s demon. Part II. From Szilard to Landauer and beyond","volume":"Volume 30","author":"Earman","year":"1999","journal-title":"Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.shpsb.2011.05.002","article-title":"Waiting for Landauer","volume":"Volume 42","author":"Norton","year":"2011","journal-title":"Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.shpsb.2013.02.005","article-title":"Landauer defended: Reply to Norton","volume":"Volume 44","author":"Ladyman","year":"2013","journal-title":"Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bormashenko, E. (2019). The Landauer principle: Re-formulation of the second thermodynamics law or a step to great unification?. Entropy, 21.","DOI":"10.20944\/preprints201908.0060.v1"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1017\/psa.2023.58","article-title":"Is thermodynamics subjective?","volume":"Volume 90","author":"Robertson","year":"2023","journal-title":"Philosophy of Science"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1080\/00207179208934253","article-title":"Stability of motion: General problem","volume":"55","author":"Lyapunov","year":"1992","journal-title":"Int. J. Control"},{"key":"ref_15","unstructured":"Feynman, R.P. (1967). Feynman Lectures on Physics, California Institute of Technology. Chapter 46."},{"key":"ref_16","unstructured":"Gibbs, J.W. (1902). Elementary Principles of Statistical Mechanics, Charles Scribner\u2019s Sons."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bormashenko, E. (2019). Generalization of the Landauer Principle for computing devices based on many-valued logic. Entropy, 21.","DOI":"10.20944\/preprints201910.0095.v1"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/3\/203\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:05:33Z","timestamp":1760105133000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/3\/203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,27]]},"references-count":17,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["e26030203"],"URL":"https:\/\/doi.org\/10.3390\/e26030203","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2024,2,27]]}}}