{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T03:02:47Z","timestamp":1773370967139,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2014,1,24]],"date-time":"2014-01-24T00:00:00Z","timestamp":1390521600000},"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>I explore the reduction of thermodynamics to statistical mechanics by treating the former as a control theory: A theory of which transitions between states can be induced on a system (assumed to obey some known underlying dynamics) by means of operations from a fixed list. I recover the results of standard thermodynamics in this framework on the assumption that the available operations do not include measurements which affect subsequent choices of operations. I then relax this assumption and use the framework to consider the vexed questions of Maxwell\u2019s demon and Landauer\u2019s principle. Throughout, I assume rather than prove the basic irreversibility features of statistical mechanics, taking care to distinguish them from the conceptually distinct assumptions of thermodynamics proper.<\/jats:p>","DOI":"10.3390\/e16020699","type":"journal-article","created":{"date-parts":[[2014,1,24]],"date-time":"2014-01-24T11:30:50Z","timestamp":1390563050000},"page":"699-725","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Thermodynamics as Control Theory"],"prefix":"10.3390","volume":"16","author":[{"given":"David","family":"Wallace","sequence":"first","affiliation":[{"name":"Balliol College, Oxford OX1 3BJ, UK"}]}],"member":"1968","published-online":{"date-parts":[[2014,1,24]]},"reference":[{"key":"ref_1","unstructured":"In fact, the etymology of thermodynamics according to the Oxford English Dictionary, is just that it is the study of heat (thermo) and work (dynamics) and their interaction. (I am grateful to Jos Uffink for this observation.)."},{"key":"ref_2","unstructured":"Wallace, D. (2014). The Non-Problem of Gibbs vs. Boltzmann Entropy, unpublished work."},{"key":"ref_3","unstructured":"Wallace, D. (2014). There are No Statistical-Mechanical Probabilities, unpublished work."},{"key":"ref_4","unstructured":"Wallace, D. (2013). Inferential vs dynamical conceptions of physics, arXiv:1306.4907v1."},{"key":"ref_5","unstructured":"Strictly speaking there is generally no finite time after which the system has exactly equilibrated, but for any given level of approximation there will be a timescale after which the system has equilibrated to within that level."},{"key":"ref_6","unstructured":"Wallace, D. (2014). What Statistical Mechanics Actually Does. unpublished work."},{"key":"ref_7","unstructured":"This is my own formulation of the argument, but I do not claim any particular originality for it; for an argument along similar lines, see [30] (pp.541\u2013548)."},{"key":"ref_8","unstructured":"An anonymous reviewer (to whom I\u2019m grateful for prompting me to clarify the preceding argument) queries whether the argument is in any case necessary (this is one thermodynamic fact the readership will take for granted). But notice that what is derived here is not really a thermodynamic fact but a statistical-mechanical one, providing the statistical-mechanical underpinning to one of the basic assumptions of phenomenological thermodynamics."},{"key":"ref_9","unstructured":"See, e. g. [31] (ch.XVII sections 10\u201314) or [32] (pp. 193\u2013196)."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0370-1573(98)00082-9","article-title":"The physics and mathematics of the second law of thermodynamics","volume":"310","author":"Lieb","year":"1999","journal-title":"Phys. Rep"},{"key":"ref_11","unstructured":"The canonical distribution can be characterised as the distribution which maximises Gibbs entropy for given expected energy, so this maximum is just the entropy of that canonical distribution."},{"key":"ref_12","first-page":"103","article-title":"Uber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter wesen","volume":"53","author":"Feld","year":"1972","journal-title":"The Collected Works of Leo Szilard: Scientific Papers"},{"key":"ref_13","unstructured":"The name one-molecule is a little unfortunate: the \u201cmolecule\u201d here is monatomic and lacks internal degrees of freedom."},{"key":"ref_14","unstructured":"An anonymous referee worries that something is wrong here: \u201cI cannot convert heat to work merely by discovering where I left the car keys\u201d. However, I can convert heat to work (more accurately: increase by capability for turning heat into work) merely by remembering which side of the partition I left my one-molecule gas; that I cannot do this with my car keys relies on mundane features of their non-isolated state and macroscopic scale."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4731","DOI":"10.1103\/PhysRevA.40.4731","article-title":"Algorithmic randomness and physical entropy","volume":"40","author":"Zurek","year":"1989","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Albert, D.Z. (2000). Time and Chance, Harvard University Press.","DOI":"10.4159\/9780674020139"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hemmo, M., and Shenker, O. (2012). The Road to Maxwell\u2019s Demon: Conceptual Foundations of Statistical Mechanics, Cambridge University Press.","DOI":"10.1017\/CBO9781139095167"},{"key":"ref_18","unstructured":"Several of these accounts (notably [16,17] use a Boltzmannian setup for statistical mechanics (I am grateful to an anonymous referee for pressing this point). I argue in [2] that nothing very deep hangs on the decision to do so; in this context, the main point to note is that Boltzmann, unlike Gibbs, entropy is not reduced by measurement, but rather, measurement gives us the capacity to perform a subsequent entropy-reducing control operation which could not be carried out if our only information about the system was its macrostate and the standard probability distribution. This illustrates the point (which I develop further in [2]) that Boltzmann entropy in the absence of additional probabilistic assumptions is almost totally uninformative about a thermodynamic system\u2019s behaviour."},{"key":"ref_19","unstructured":"For forceful defence of the idea that the practicalities are what prevents Second Law violation in these cases, see [33]."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Preskill, J. (1998). Fault-tolerant quantum computation. Introd. Quantum Comput. Inf, 213.","DOI":"10.1142\/9789812385253_0008"},{"key":"ref_21","unstructured":"Shor, P.W. Fault-tolerant Quantum Computation. Los Alamitos, California."},{"key":"ref_22","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. Mod. Phys"},{"key":"ref_23","unstructured":"Zalta, E.N. (2009). Stanford Encyclopedia of Philosophy, Available online: http:\/\/plato.stanford.edu\/archives\/fall2009\/entries\/information-entropy\/."},{"key":"ref_24","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. Mod. Phys"},{"key":"ref_25","unstructured":"Leff, H., and Rex, A.F. (2002). Maxwell\u2019s Demon: Entropy, Information, Computing, Institute of Physics Publishing. [2nd ed.]."},{"key":"ref_26","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_27","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_28","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_29","unstructured":"Norton, J. Waiting for Landauer. Available online: http:\/\/philsci-archive.pitt.edu\/8635\/."},{"key":"ref_30","unstructured":"Tolman, R.C. (1938). The Principles of Statistical Mechanics, Oxford University Press."},{"key":"ref_31","unstructured":"Messiah, A. (1962). Quantum Mechanics, Volume II, North-Holland Publishing Company."},{"key":"ref_32","unstructured":"Weinberg, S. (2013). Quantum Mechanics, Cambridge University Press."},{"key":"ref_33","unstructured":"Norton, J. The End of the Thermodynamics of Computation: A no go Result. San Diego, CA, USA. Available online: http:\/\/philsci-archive.pitt.edu\/9658\/."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/2\/699\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:07:40Z","timestamp":1760216860000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/2\/699"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,24]]},"references-count":33,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,2]]}},"alternative-id":["e16020699"],"URL":"https:\/\/doi.org\/10.3390\/e16020699","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,24]]}}}