{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T15:38:14Z","timestamp":1783697894378,"version":"3.55.0"},"reference-count":55,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T00:00:00Z","timestamp":1766793600000},"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 link between information and energy introduces the observer and their knowledge into the understanding of a fundamental quantity in physics. Two approaches compete to account for this link\u2014Brillouin\u2019s negentropy law of information and Landauer\u2019s law on data erasure\u2014which are often confused. The first, based on Clausius\u2019 inequality and Shannon\u2019s mathematical results, is very robust, whereas the second, based on the simple idea that information requires a material embodiment (data bits), is now perceived as more physical and therefore prevails. In this paper, we show that Landauer\u2019s idea results from a confusion between information (a global emergent concept) and data (a local material object). This confusion leads to many inconsistencies and is incompatible with thermodynamics and information theory. The reason it prevails is interpreted as being due to a frequent tendency of materialism towards reductionism, neglecting emergence and seeking to eliminate the role of the observer. A paradoxical trend, considering that it is often accompanied by the materialist idea that all scientific knowledge, nevertheless, originates from observation. Information and entropy are actually emergent quantities introduced in the theory by convention.<\/jats:p>","DOI":"10.3390\/e28010037","type":"journal-article","created":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T06:25:51Z","timestamp":1766989551000},"page":"37","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Disentangling Brillouin\u2019s Negentropy Law of Information and Landauer\u2019s Law on Data Erasure"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9443-5029","authenticated-orcid":false,"given":"Didier","family":"Lairez","sequence":"first","affiliation":[{"name":"Laboratoire des Solides Irradi\u00e9s, \u00c9cole Polytechnique, CEA, CNRS, IPP, 91128 Palaiseau, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,27]]},"reference":[{"key":"ref_1","unstructured":"Feynman, R.P., Leighton, R.B., and Sands, M. (1966). The Feynman Lectures on Physics, Addison-Wesley. Chapter 4."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1119\/1.2432084","article-title":"Energy and Change","volume":"45","author":"Hecht","year":"2007","journal-title":"Phys. Teach."},{"key":"ref_3","unstructured":"Maxwell, J.C. (1872). Theory of Heat, Longmans, Green and Co.. [3rd ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_5","unstructured":"Gibbs, J. (1902). Elementary Principles in Statistical Mechanics, Charles Scribner\u2019s Sons."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1063\/1.1721463","article-title":"The Negentropy Principle of Information","volume":"24","author":"Brillouin","year":"1953","journal-title":"J. Appl. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Brillouin, L. (1956). Science and Information Theory, Dover Publications.","DOI":"10.1063\/1.3059856"},{"key":"ref_8","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. Dev."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/0375-9601(96)00453-7","article-title":"The physical nature of information","volume":"217","author":"Landauer","year":"1996","journal-title":"Phys. Lett. A"},{"key":"ref_11","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_12","doi-asserted-by":"crossref","unstructured":"Herrera, L. (2020). Landauer Principle and General Relativity. Entropy, 22.","DOI":"10.3390\/e22030340"},{"key":"ref_13","unstructured":"Hahn, H., Neurath, O., and Carnap, R. (1973). The scientific conception of the world: The Vienna Circle. Empiricism and Sociology, Springer."},{"key":"ref_14","unstructured":"Mach, E. (1911). History and Root of the Principle of the Conservation of Energy, The Open Court Publishing Company."},{"key":"ref_15","unstructured":"Mach, E. (1919). The Science of Mechanics, The Open Court Publishing Company."},{"key":"ref_16","unstructured":"Carnap, R. (1966). Philosophical Foundations of Physics, Basic Books."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Duhem, P. (2021). The Aim and Structure of Physical Theory, Princeton University Press.","DOI":"10.2307\/j.ctv1nj34vm"},{"key":"ref_18","unstructured":"Poincar\u00e9, H. (1905). Science and Hypothesis, The Walter Scott Publishing Co."},{"key":"ref_19","unstructured":"Poincar\u00e9, H. (1907). The Value of Science, The Science Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1086\/286316","article-title":"On the method of theoretical physics","volume":"1","author":"Einstein","year":"1934","journal-title":"Philos. Sci."},{"key":"ref_21","first-page":"625","article-title":"Diffusion","volume":"2","author":"Maxwell","year":"1878","journal-title":"Encycl. Br. Reprod. Sci. Pap."},{"key":"ref_22","unstructured":"Lairez, D. (2022). A short derivation of Boltzmann distribution and Gibbs entropy formula from the fundamental postulate. arXiv."},{"key":"ref_23","unstructured":"(2025, November 30). Entropy, Special Issue \u2018Gibbs Paradox and Its Resolutions\u2019. Available online: https:\/\/www.mdpi.com\/journal\/entropy\/special_issues\/gibbs_paradox."},{"key":"ref_24","unstructured":"(2025, November 30). Entropy, Special Issue \u2018Gibbs Paradox 2018\u2019. Available online: https:\/\/www.mdpi.com\/journal\/entropy\/special_issues\/Gibbs_Paradox_2018."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Gibbs, J.W. (1874). On the Equilibrium of Heterogeneous Substances: First [-Second] Part, Connecticut Academy of Arts and Sciences.","DOI":"10.5479\/sil.421748.39088007099781"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lairez, D. (2024). Thermostatistics, Information, Subjectivity: Why Is This Association So Disturbing?. Mathematics, 12.","DOI":"10.3390\/math12101498"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Lairez, D. (2023). Plea for the use of the exact Stirling formula in statistical mechanics. SciPost Physics Lecture Notes, 76.","DOI":"10.21468\/SciPostPhysLectNotes.76"},{"key":"ref_28","unstructured":"Callen, H.B. (1985). Thermodynamics and an Introduction to Thermostatistics, J. Wiley & Sons. [2nd ed.]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1007\/BF02392508","article-title":"Chapitre II. Th\u00e9orie des invariants int\u00e9graux","volume":"13","year":"1890","journal-title":"Acta Math."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Balian, R. (1991). From Microphysics to Macrophysics, Springer.","DOI":"10.1007\/978-3-540-45475-5"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1086\/286754","article-title":"The principle of insufficient reason","volume":"9","author":"Dubs","year":"1942","journal-title":"Philos. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1080\/14786445008646622","article-title":"Remarks on an alleged proof of the \u201cMethod of least squares,\u201d contained in a late number of the Edinburgh review","volume":"37","author":"Ellis","year":"1850","journal-title":"Lond. Edinb. Dublin Philos. Mag. J. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information theory and statistical mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1103\/PhysRev.108.171","article-title":"Information theory and statistical mechanics. II","volume":"108","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/TIT.1980.1056144","article-title":"Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy","volume":"26","author":"Shore","year":"1980","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/BF00709116","article-title":"The well-posed problem","volume":"3","author":"Jaynes","year":"1973","journal-title":"Found. Phys."},{"key":"ref_37","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. Sci."},{"key":"ref_38","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":"30","author":"Earman","year":"1999","journal-title":"Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1038\/nphys1821","article-title":"Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality","volume":"6","author":"Toyabe","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_40","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_41","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_42","doi-asserted-by":"crossref","first-page":"e1501492","DOI":"10.1126\/sciadv.1501492","article-title":"Experimental test of Landauer\u2019s principle in single-bit operations on nanomagnetic memory bits","volume":"2","author":"Hong","year":"2016","journal-title":"Sci. Adv."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Ciliberto, S., and Lutz, E. (2018). The physics of information: From Maxwell to Landauer. Energy Limits in Computation, Springer International Publishing.","DOI":"10.1007\/978-3-319-93458-7_5"},{"key":"ref_44","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_45","doi-asserted-by":"crossref","unstructured":"Lairez, D. (2023). Thermodynamical versus Logical Irreversibility: A Concrete Objection to Landauer\u2019s Principle. Entropy, 25.","DOI":"10.20944\/preprints202307.0421.v1"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Lairez, D. (2024). On the Supposed Mass of Entropy and That of Information. Entropy, 26.","DOI":"10.3390\/e26040337"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Lairez, D. (2024). The Fundamental Difference Between Boolean Logic and Thermodynamic Irreversibilities, or, Why Landauer\u2019s Result Cannot Be a Physical Principle. Symmetry, 16.","DOI":"10.3390\/sym16121594"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.shpsb.2004.11.006","article-title":"The (absence of a) relationship between thermodynamic and logical reversibility","volume":"36","author":"Maroney","year":"2005","journal-title":"Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys."},{"key":"ref_49","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. Sci. Part B Stud. Hist. Philos. Mod. Phys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1450002","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_51","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_52","doi-asserted-by":"crossref","first-page":"035311","DOI":"10.1063\/5.0087175","article-title":"Experimental protocol for testing the mass-energy-information equivalence principle","volume":"12","author":"Vopson","year":"2022","journal-title":"AIP Adv."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Bishop, R.C. (2024). Brief history of the debate. The Physics of Emergence (Second Edition), IOP Publishing.","DOI":"10.1088\/978-0-7503-6367-9"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Baggio, G., and Parravicini, A. (2019). Introduction to Pragmatism and Theories of Emergence. Eur. J. Pragmatism Am. Philos., XI-2.","DOI":"10.4000\/ejpap.1611"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"143","DOI":"10.5840\/eip2002325","article-title":"Emergence Theories and Pragmatic Realism","volume":"3","year":"2002","journal-title":"Essays Philos."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/1\/37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T06:28:40Z","timestamp":1766989720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/1\/37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,27]]},"references-count":55,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["e28010037"],"URL":"https:\/\/doi.org\/10.3390\/e28010037","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,27]]}}}