{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T21:00:09Z","timestamp":1773003609267,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T00:00:00Z","timestamp":1574640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Landauer principle asserts that \u201cthe information is physical\u201d. In its strict meaning, Landauer\u2019s principle states that there is a minimum possible amount of energy required to erase one bit of information, known as the Landauer bound     W =  k B  T l n 2    , where T is the temperature of a thermal reservoir used in the process and      k B      is Boltzmann\u2019s constant. Modern computers use the binary system in which a number is expressed in the base-2 numeral system. We demonstrate that the Landauer principle remains valid for the physical computing device based on the ternary, and more generally, N-based logic. The energy necessary for erasure of one bit of information (the Landauer bound)     W =  k B  T l n 2     remains untouched for the computing devices exploiting a many-valued logic.<\/jats:p>","DOI":"10.3390\/e21121150","type":"journal-article","created":{"date-parts":[[2019,11,25]],"date-time":"2019-11-25T11:12:21Z","timestamp":1574680341000},"page":"1150","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Generalization of the Landauer Principle for Computing Devices Based on Many-Valued Logic"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1356-2486","authenticated-orcid":false,"given":"Edward","family":"Bormashenko","sequence":"first","affiliation":[{"name":"Department of Chemical Engineering, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/MAHC.2005.49","article-title":"The ternary calculating machine of Thomas Fowler","volume":"27","author":"Glusker","year":"2005","journal-title":"IEEE Ann. Hist. Comput."},{"key":"ref_2","first-page":"39","article-title":"An experience of the ternary computer development","volume":"2","author":"Brousentsov","year":"1965","journal-title":"Bull. Mosc. Univ. Math. Mech."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1093\/comjnl\/45.2.221","article-title":"Brousentsov\u2019s ternary principle, Bergman\u2019s number system and ternary mirror-symmetrical arithmetic","volume":"45","author":"Stakhov","year":"2005","journal-title":"Comput. J."},{"key":"ref_4","unstructured":"Gottwald, Z. (2001). A Treatise on Many-Valued Logics (Studies in Logic and Computation), Kings College London."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1090\/S0002-9947-1958-0094302-9","article-title":"Algebraic analysis of many valued logics","volume":"88","author":"Chang","year":"1958","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_6","unstructured":"Frieder, G., Fong, A., and Chao, C.Y. (1973, January 24\u201325). A Balanced Ternary Computer. Proceedings of the 1973 International Symposium on Multiple-valued Logic, Toronto, ON, Canada."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1147\/rd.53.0183","article-title":"Dissipation and heat generation in the computing process","volume":"5","author":"Landauer","year":"1961","journal-title":"IBM J. Res. Dev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1063\/1.881299","article-title":"Information is physical","volume":"44","author":"Landauer","year":"1991","journal-title":"Phys. Today"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1914","DOI":"10.1126\/science.272.5270.1914","article-title":"Minimal energy requirements in communication","volume":"272","author":"Landauer","year":"1996","journal-title":"Science"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/nphys3230","article-title":"Thermodynamics of information","volume":"11","author":"Parrondo","year":"2015","journal-title":"Nature Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103011","DOI":"10.1088\/1367-2630\/16\/10\/103011","article-title":"An improved Landauer principle with finite-size corrections","volume":"16","author":"Reeb","year":"2004","journal-title":"New J. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"40004","DOI":"10.1209\/0295-5075\/95\/40004","article-title":"Second law and Landauer principle far from equilibrium","volume":"95","author":"Esposito","year":"2011","journal-title":"EPL"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"060602","DOI":"10.1103\/PhysRevLett.114.060602","article-title":"Nonequilibrium quantum Landauer Principle","volume":"114","author":"Goold","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"030102","DOI":"10.1103\/PhysRevE.83.030102","article-title":"Landauer\u2019s principle in the quantum regime","volume":"83","author":"Hilt","year":"2011","journal-title":"Phys. Rev. E."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Herrera, L. (2017). The Gibbs Paradox, the Landauer Principle and the irreversibility associated with tilted observers. Entropy, 19.","DOI":"10.3390\/e19030110"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"14500","DOI":"10.1142\/S0219477514500023","article-title":"The mass of a bit of information and the Brillouin\u2019s Principle","volume":"13","author":"Herrera","year":"2014","journal-title":"Fluct. Noise Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.physleta.2006.10.027","article-title":"Forgetting and gravitation: From Landauer\u2019s principle to Tolman\u2019s temperature","volume":"362","author":"Daffertshofer","year":"2007","journal-title":"Phys. Lett. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"095206","DOI":"10.1063\/1.5123794","article-title":"The mass-energy-information equivalence principle","volume":"9","author":"Vopson","year":"2019","journal-title":"AIP Adv."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1007\/BF01341281","article-title":"\u00dcber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen","volume":"53","author":"Szilard","year":"1929","journal-title":"Z. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1063\/PT.3.2912","article-title":"Information: From Maxwell\u2019s demon to Landauer\u2019s eraser","volume":"68","author":"Lutz","year":"2015","journal-title":"Phys. Today"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1119\/1.2757626","article-title":"The Carnot engine based on the small thermodynamic system: Its efficiency and the ergodic hypothesis","volume":"75","author":"Bormashenko","year":"2007","journal-title":"Am. J. Phys."},{"key":"ref_22","first-page":"569","article-title":"Maxwell\u2019s Demon and the thermodynamics of computation. Maxwell\u2019s Demon and the thermodynamics of computation","volume":"32","author":"Bub","year":"2000","journal-title":"Stud. Hist. Philos. Sci. B"},{"key":"ref_23","first-page":"7388","article-title":"Experimental verification of Landauer\u2019s principle linking information and thermodynamics","volume":"483","author":"Arakelyan","year":"2012","journal-title":"Nature"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"190601","DOI":"10.1103\/PhysRevLett.113.190601","article-title":"High-Precision test of Landauer\u2019s Principle in a feedback trap","volume":"113","author":"Jun","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1038\/s41567-018-0070-7","article-title":"Quantum Landauer erasure with a molecular nanomagnet","volume":"14","author":"Gaudenzi","year":"2018","journal-title":"Nat. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"210601","DOI":"10.1103\/PhysRevLett.120.210601","article-title":"Single-atom demonstration of the quantum Landauer principle","volume":"120","author":"Yan","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"12068","DOI":"10.1038\/ncomms12068","article-title":"Sub-kBT micro-electromechanical irreversible logic gate","volume":"7","author":"Neri","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1620001","DOI":"10.1142\/S0219477516200017","article-title":"Comments on \u201cSub-kBT micro-electromechanical irreversible logic gate\u201d","volume":"15","author":"Kish","year":"2016","journal-title":"Fluct. Noise Lett."},{"key":"ref_29","unstructured":"Knuth, D.E. (1998). The Art of Computer Programming: Seminumerical Algorithms, Addison Wesley. [3rd ed.]."},{"key":"ref_30","first-page":"375","article-title":"Eaters of the lotus: Landauer\u2019s principle and the return of Maxwell\u2019s demon","volume":"36","author":"Norton","year":"2005","journal-title":"Stud. Hist. Philos. Sci. B"},{"key":"ref_31","first-page":"184","article-title":"Waiting for Landauer","volume":"42","author":"Norton","year":"2011","journal-title":"Stud. Hist. Philos. Sci. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/S1355-2198(03)00039-X","article-title":"Notes on Landauer\u2019s principle, reversible computation, and Maxwell\u2019s Demon","volume":"34","author":"Bennett","year":"2003","journal-title":"Stud. Hist. Philos. Mod. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Nosonovsky, M., and Breki, A.D. (2019). Ternary logic of motion to resolve kinematic frictional paradoxes. Entropy, 21.","DOI":"10.3390\/e21060620"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/12\/1150\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:37:22Z","timestamp":1760189842000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/12\/1150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,25]]},"references-count":33,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["e21121150"],"URL":"https:\/\/doi.org\/10.3390\/e21121150","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201910.0095.v1","asserted-by":"object"}]},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,25]]}}}