{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:40:19Z","timestamp":1760244019291,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2009,10,13]],"date-time":"2009-10-13T00:00:00Z","timestamp":1255392000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Landauer\u2019s principle is one of the pillars of the physics of information. It constitutes one of the foundations behind the idea that \u201cinformation is physical\u201d. Landauer\u2019s principle establishes the smallest amount of energy that has to be dissipated when one bit of information is erased from a computing device. Here we explore an extended Landauerlike principle valid for general dynamical systems (not necessarily Hamiltonian) governed by divergenceless phase space flows.<\/jats:p>","DOI":"10.3390\/e11040586","type":"journal-article","created":{"date-parts":[[2009,10,13]],"date-time":"2009-10-13T10:54:58Z","timestamp":1255431298000},"page":"586-597","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Landauer\u2019s Principle and Divergenceless Dynamical Systems"],"prefix":"10.3390","volume":"11","author":[{"given":"Claudia","family":"Zander","sequence":"first","affiliation":[{"name":"Physics Department, University of Pretoria, Pretoria 0002, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angel  Ricardo","family":"Plastino","sequence":"additional","affiliation":[{"name":"Physics Department, University of Pretoria, Pretoria 0002, South Africa"},{"name":"Instituto de F\u00edsica T\u00e9orica y Computacional Carlos I, Facultad de Ciencias, Universidad de Granada, Granada, Spain"},{"name":"National University La Plata, UNLP-CREG-CONICET, Casilla de Correos 727, 1900 La Plata, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angelo","family":"Plastino","sequence":"additional","affiliation":[{"name":"National University La Plata, UNLP-CREG-CONICET, Casilla de Correos 727, 1900 La Plata, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Montserrat","family":"Casas","sequence":"additional","affiliation":[{"name":"Departament de F\u00edsica, Universitat de les Illes Balears, Mallorca, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergio","family":"Curilef","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidad Cat\u00f3lica del Norte, Antofagasta, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2009,10,13]]},"reference":[{"key":"ref_1","unstructured":"Zurek, W.H. (1990). Complexity, Entropy, and the Physics of Information, Addison-Wesley."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Beck, C., and Schlogl, F. (1993). Thermodynamics of Chaotic Systems, Cambridge University Press.","DOI":"10.1017\/CBO9780511524585"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2274","DOI":"10.1103\/PhysRevE.52.2274","article-title":"Lagrangians of physics and the game of Fisher-information transfer","volume":"52","author":"Frieden","year":"1995","journal-title":"Phys. Rev. E"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Frieden, B.R. (1998). Physics from Fisher Information, Cambridge University Press.","DOI":"10.1017\/CBO9780511622670"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Frieden, B.R. (2004). Science from Fisher Information, Cambridge University Press.","DOI":"10.1017\/CBO9780511616907"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Leff, H.S., and Rex, A.F. (2003). Maxwell\u2019s Demons 2: Entropy, Classical and Quantum Information, Institute of Physics Publishing.","DOI":"10.1201\/9781420033991"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"210601","DOI":"10.1103\/PhysRevLett.88.210601","article-title":"Classical no-cloning theorem","volume":"88","author":"Daffertshofer","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"138701","DOI":"10.1103\/PhysRevLett.93.138701","article-title":"Liouville dynamics and the conservation of classical information","volume":"93","author":"Plastino","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"052108","DOI":"10.1103\/PhysRevA.74.052108","article-title":"Information-theoretic significance of the Wigner distribution","volume":"74","author":"Frieden","year":"2006","journal-title":"Phys. Rev. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2602","DOI":"10.1103\/PhysRevA.59.2602","article-title":"Universal geometric approach to uncertainty, entropy, and information","volume":"59","author":"Hall","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2861","DOI":"10.1088\/1751-8113\/40\/11\/020","article-title":"Entanglement and the speed of evolution of multi-partite quantum systems","volume":"40","author":"Zander","year":"2007","journal-title":"J. Phys. A: Math. Theor."},{"key":"ref_12","unstructured":"Rosenkrantz, R.D. (1987). Papers on Probability, Statistics and Statistical Physics, Dordrecht."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/0375-9601(93)91147-W","article-title":"Maximum entropy and approximate descriptions of pure states","volume":"181","author":"Plastino","year":"1993","journal-title":"Phys. Lett. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3927","DOI":"10.1103\/PhysRevE.56.3927","article-title":"Minimum Kullback entropy approach to the Fokker-Planck equation","volume":"56","author":"Plastino","year":"1997","journal-title":"Phys. Rev. E"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Loewenstein, W.R. (1999). The Touchstone of Life: Molecular Information, Cell Communication, and the Foundations of Life, Oxford University Press.","DOI":"10.1093\/oso\/9780195118285.001.0001"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1038\/23376","article-title":"Rolf Landauer: Head and heart of the physics of information","volume":"400","author":"Lloyd","year":"1999","journal-title":"Nature"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1147\/rd.53.0183","article-title":"Irreversibility and heat generation in the computing process","volume":"5","author":"Landauer","year":"1961","journal-title":"IBM J. Res. Develop."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"062314","DOI":"10.1103\/PhysRevA.61.062314","article-title":"Information erasure","volume":"61","author":"Piechocinska","year":"2000","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.physleta.2005.05.058","article-title":"Landauer\u2019s principle and the conservation of information","volume":"342","author":"Daffertshofer","year":"2005","journal-title":"Phys. Lett. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2341","DOI":"10.1016\/j.physleta.2007.11.055","article-title":"Landauer\u2019s principle and non-equilibrium statistical ensembles","volume":"372","author":"Curilef","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1080\/00107510010018916","article-title":"The physics of forgetting: Landauers erasure principle and information theory","volume":"42","author":"Plenio","year":"2001","journal-title":"Contemp. Phys."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","unstructured":"Smale, S. (1980). Nonlinear Dynamics, Annals of New York Academy of Sciences 357, New York Academy of Sciences.","DOI":"10.1111\/j.1749-6632.1980.tb29691.x"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0378-4371(99)00217-4","article-title":"Dynamical thermostatting, divergenceless phase-space flows, and KBB systems","volume":"271","author":"Plastino","year":"1999","journal-title":"Physica A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1140\/epjb\/e2005-00372-3","article-title":"Dynamical thermostatting and statistical ensembles","volume":"48","author":"Roston","year":"2005","journal-title":"Eur. Phys. J. B"},{"key":"ref_26","unstructured":"Kerner, E.H. (1972). Gibbs Ensemble, Biological Ensemble, Gordon and Breach."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/0375-9601(90)90911-7","article-title":"Note on Hamiltonian format of Lotka-Volterra dynamics","volume":"151","author":"Kerner","year":"1990","journal-title":"Phys. Lett. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1103\/PhysRevD.7.2405","article-title":"Generalized hamiltonian dynamics","volume":"7","author":"Nambu","year":"1973","journal-title":"Phys. Rev. D"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/0375-9601(91)90458-K","article-title":"Quantum mechanics as a generalization of Nambu dynamics to the Weyl-Wigner formalism","volume":"158","author":"Morrison","year":"1991","journal-title":"Phys. Lett. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1088\/0305-4470\/27\/7\/031","article-title":"Developments in Nambu mechanics","volume":"27","author":"Codriansky","year":"1994","journal-title":"J. Phys. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1016\/0378-4371(96)00140-9","article-title":"Statistical treatment of autonomous systems with divergencelless flows","volume":"232","author":"Plastino","year":"1996","journal-title":"Physica A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1006\/aphy.2001.6159","article-title":"Generalized lorentz-force equations","volume":"292","author":"Yamaleev","year":"2001","journal-title":"Ann. Phys. N. Y."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4035","DOI":"10.1063\/1.1481955","article-title":"Applications of Nambu mechanics to systems of hydrodynamical type","volume":"43","author":"Guha","year":"2002","journal-title":"J. Math. Phys-NY"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1103\/RevModPhys.50.221","article-title":"General properties of entropy","volume":"50","author":"Wehrl","year":"1978","journal-title":"Rev. Mod. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/S0378-4371(03)00019-0","article-title":"Superstatistics","volume":"322","author":"Beck","year":"2003","journal-title":"Physica A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.physa.2004.06.001","article-title":"Superstatistical generalization of the work fluctuation theorem","volume":"344","author":"Beck","year":"2004","journal-title":"Physica A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"064502","DOI":"10.1103\/PhysRevLett.98.064502","article-title":"Statistics of three-dimensional lagrangian turbulence","volume":"98","author":"Beck","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1143\/PTPS.162.87","article-title":"Thermodynamical and informational structure of superstatistics","volume":"162","author":"Yamano","year":"2006","journal-title":"Prog. Theor. Phys. 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