{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:29:05Z","timestamp":1761611345518,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2014,4,22]],"date-time":"2014-04-22T00:00:00Z","timestamp":1398124800000},"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>There seems to be a consensus among physicists that there is a connection between information processing and thermodynamics. In particular, Landauer\u2019s Principle (LP) is widely assumed as part of the foundation of information theoretic\/computational reasoning in diverse areas of physics including cosmology. It is also often appealed to in discussions about Maxwell\u2019s demon and the status of the Second Law of Thermodynamics. However, LP has been challenged. In his 2005, Norton argued that LP has not been proved. LPSG offered a new proof of LP. Norton argued that the LPSG proof is unsound and Ladyman and Robertson defended it. However, Norton\u2019s latest work also generalizes his critique to argue for a no go result that he purports to be the end of the thermodynamics of computation. Here we review the dialectic as it currently stands and consider Norton\u2019s no go result.<\/jats:p>","DOI":"10.3390\/e16042278","type":"journal-article","created":{"date-parts":[[2014,4,22]],"date-time":"2014-04-22T12:18:37Z","timestamp":1398169117000},"page":"2278-2290","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Going Round in Circles: Landauer vs. Norton on the Thermodynamics of Computation"],"prefix":"10.3390","volume":"16","author":[{"given":"James","family":"Ladyman","sequence":"first","affiliation":[{"name":"Department of Philosophy, University of Bristol, Cotham House, Cotham Hill, Bristol BS6 6JL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katie","family":"Robertson","sequence":"additional","affiliation":[{"name":"Faculty of Philosophy, Radcliffe Humanities, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,4,22]]},"reference":[{"key":"ref_1","unstructured":"Landau, L.D., and Lifshitz, E.M. (1958). Statistical Physics, Pergamon Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1007\/BF01341281","article-title":"Uber die Entropieverminderung in einem thermodynamischen system Bei Eingriffen intelligenter wesen","volume":"5","author":"Szilard","year":"1929","journal-title":"Zeitschr. Phys"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1147\/rd.176.0525","article-title":"The logical reversibility of computation","volume":"17","author":"Bennett","year":"1973","journal-title":"IBM J. Res. Dev"},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1007\/BF02084158","article-title":"The thermodynamics of computation\u2014A review","volume":"21","author":"Bennett","year":"1982","journal-title":"Int. J. Theor. Phys"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1038\/scientificamerican1187-108","article-title":"Demons, engines and the second law","volume":"257","author":"Bennett","year":"1987","journal-title":"Sci. Am"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1147\/rd.321.0016","article-title":"Notes on the history of reversible computation","volume":"32","author":"Bennett","year":"1988","journal-title":"IBM J. Res. Dev"},{"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","unstructured":"Blundell, S., and Blundell, K. (2010). Concepts in Thermal Physics, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199562091.001.0001"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.shpsb.2004.12.002","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. Mod. Phys"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.shpsb.2006.03.007","article-title":"The connection between logical and thermodynamic irreversibility","volume":"38","author":"Ladyman","year":"2007","journal-title":"Stud. Hist. Philos. Mod. Phys"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.shpsb.2011.05.002","article-title":"Waiting for Landauer","volume":"42","author":"Norton","year":"2011","journal-title":"Stud. Hist. Philos. Mod. Phys"},{"key":"ref_13","first-page":"263","article-title":"Landauer defened: Reply to Norton","volume":"44","author":"Ladyman","year":"2013","journal-title":"Stud. Hist. Philos. Sci. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1086\/673714","article-title":"The end of the thermodynamics of computation: A no go result","volume":"80","author":"Norton","year":"2013","journal-title":"Philos. Sci"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4432","DOI":"10.3390\/e15104432","article-title":"All shook up: Fluctuations, Maxwell\u2019s demon and the thermodynamics of computation","volume":"15","author":"Norton","year":"2013","journal-title":"Entropy"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Maudlin, T. (2011). Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics, Wiley-Blackwell. [3rd ed].","DOI":"10.1002\/9781444396973"},{"key":"ref_17","unstructured":"Hey, J.G., and Allen, W. (1996). Feynman Lectures on Computation, Addison-Wesley."},{"key":"ref_18","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_19","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.shpsb.2007.11.004","article-title":"The use of the information-theoretic entropy in thermodynamics","volume":"39","author":"Ladyman","year":"2008","journal-title":"Stud. Hist. Philos. Mod. Phys"},{"key":"ref_20","unstructured":"A controlled operation of a degree of freedom onto itself is one where the form of the operation depends on the state of the degree of freedom and nothing else. As Ladyman and Robertson argue, it is trivial that LP is false if such operations are admitted, and controlled operations such as CNOT require a control system and a target system that consist of different physical degrees of freedom so that the state of the former can vary independently of the state of the latter prior to the operation being implemented."},{"key":"ref_21","unstructured":"Norton\u2019s arguments for the no-go result in this volume do not make reference to the Einstein-Tolman method. Some but not all of our criticisms here apply only to his argument in his 2011 and forthcoming a. We do not consider Norton forthcoming b here."},{"key":"ref_22","unstructured":"Hence, sometimes \u201cquasi-static\u201d is used to refer to processes that involve a sequence of states each of which is almost at equilibrium (see for example [25] (p. 243))."},{"key":"ref_23","unstructured":"Tolman, R. (1938). The Principles of Statistical Mechanics, Clarendon Press."},{"key":"ref_24","unstructured":"P(being in a state compatible with the control)= P(fluctuating to the state at the control value) is approximately valid when the control value is near the mean value."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Cowan, B. (2005). Topics in Statistical Mechanics, Imperical College Press.","DOI":"10.1142\/p392"},{"key":"ref_26","unstructured":"In any computational device the physical states that represent computational states are likely to be coarse-grained with respect to the underlying fundamental physical state. For example, in a standard logic gate the computational states are represented by potential differences, and all that matters is whether they are either approximately 0V or approximately 3V, and so all manner of fluctuations in the exact physical state of the system are compatible with the computation proceeding in a particular way. Even in a molecular scale computation fluctuations in the exact state of the system will be permissible providing that they are compatible with the reliable evolution of the system in such a way as to take the relevant physical input states to the relevant physical output states so as to implement the computation. Of course, one can also consider probabilistic computation where some aspects of the computation proceed non-deterministically, however in the present context it is deterministic computation that is at issue. This does not mean that the underlying physics must be deterministic in toto, just that the system will follow the appropriate time evolution at the scale of the physical states used to represent computational states so that the computation can be reliably implemented."},{"key":"ref_27","unstructured":"Friedman, M. (2001). Dynamics of Reason, Chicago University Press."},{"key":"ref_28","unstructured":"Berut et al. [29] claim to have experimentally verified LP. However, Norton [15] (Section 3.7) argues that their \u201cerasure protocol\u201d includes an unnecessary step that involves dissipation, and also that LP is not tested since the entropy associated with the heat produced by the whole apparatus is not taken into account."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1038\/nature10872","article-title":"Experimental verification of Landauer\u2019s principle linking information and thermodynamics","volume":"483","author":"Berut","year":"2012","journal-title":"Nature"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/4\/2278\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:10:35Z","timestamp":1760217035000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/4\/2278"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,22]]},"references-count":29,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,4]]}},"alternative-id":["e16042278"],"URL":"https:\/\/doi.org\/10.3390\/e16042278","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2014,4,22]]}}}