Editing Maxwell's demon (section)

== Criticism and development ==
Several physicists have presented calculations that show that the [[second law of thermodynamics]] will not actually be violated, if a more complete analysis is made of the whole system including the demon.<ref name="Bennett87" /><ref name="Sagawa" /><ref name="BennettSchumacher">{{cite journal|last1 = Bennett|first1 = Charles H.|last2 = Schumacher|first2 = Benjamin|title = Maxwell's demons appear in the lab|journal = Nikkei Science|pages = 3–6|date = August 2011|url = http://www.nikkei-science.com/wp-content/uploads/2011/08/201108_032.pdf|access-date = November 13, 2014}}</ref> The essence of the physical argument is to show, by calculation, that any demon must "generate" more entropy segregating the molecules than it could ever eliminate by the method described. That is, it would take more thermodynamic work to gauge the speed of the molecules and selectively allow them to pass through the opening between ''A'' and ''B'' than the amount of [[energy]] gained by the difference of temperature caused by doing so.

One of the most famous responses to this question was suggested in 1929 by [[Leó Szilárd]],<ref name="Szilard">{{cite journal|last = Szilard|first = Leo|title = Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen (On the reduction of entropy in a thermodynamic system by the intervention of intelligent beings)|journal = Zeitschrift für Physik|volume = 53|issue = 11–12|pages = 840–856|date = 1929|doi = 10.1007/bf01341281|bibcode = 1929ZPhy...53..840S|s2cid = 122038206}} cited in Bennett 1987. English translation available as [http://aurellem.org/jaynes/sources/Szilard.pdf NASA document TT F-16723] published 1976</ref> and later by [[Léon Brillouin]].<ref name="Bennett87" /><ref name="Sagawa" />  Szilárd pointed out that a real-life Maxwell's demon would need to have some means of measuring molecular speed, and that the act of acquiring information would require an expenditure of energy. Since the demon and the gas are interacting, we must consider the total entropy of the gas and the demon combined. The expenditure of energy by the demon will cause an increase in the entropy of the demon, which will be larger than the lowering of the entropy of the gas.

In 1960, [[Rolf Landauer]] raised an exception to this argument.<ref name="Bennett87" /><ref name="Sagawa" /><ref name="Landauer">{{cite journal|last = Landauer|first = R.|title = Irreversibility and heat generation in the computing process|journal = IBM Journal of Research and Development|volume = 5|issue = 3|pages = 183–191|date = 1961|url = http://www.pitt.edu/~jdnorton/lectures/Rotman_Summer_School_2013/thermo_computing_docs/Landauer_1961.pdf|doi = 10.1147/rd.53.0183|access-date = November 13, 2014}} reprinted in [http://domino.research.ibm.com/tchjr/journalindex.nsf/c469af92ea9eceac85256bd50048567c/8a9d4b4e96887b8385256bfa0067fba2?OpenDocument Vol. 44, No. 1, January 2000, p. 261] {{Webarchive|url=https://web.archive.org/web/20160303181021/http://domino.research.ibm.com/tchjr/journalindex.nsf/c469af92ea9eceac85256bd50048567c/8a9d4b4e96887b8385256bfa0067fba2?OpenDocument |date=2016-03-03 }}</ref>  He realized that some measuring processes need not increase thermodynamic entropy as long as they were [[Reversible process (thermodynamics)|thermodynamically reversible]]. He suggested these "reversible" measurements could be used to sort the molecules, violating the Second Law. However, due to the connection between [[entropy in thermodynamics and information theory]], this also meant that the recorded measurement must not be erased. In other words, to determine whether to let a molecule through, the demon must acquire information about the state of the molecule and either discard it or store it. Discarding it leads to immediate increase in entropy, but the demon cannot store it indefinitely. In 1982, [[Charles H. Bennett (computer scientist)|Charles Bennett]] showed that, however well prepared, eventually the demon will run out of information storage space and must begin to erase the information it has previously gathered.<ref name="Sagawa" /><ref name="Bennett82">{{Cite journal|last1 = Bennett|first1 = C. H.|title = The thermodynamics of computation—a review|doi = 10.1007/BF02084158|journal = International Journal of Theoretical Physics|volume = 21|issue = 12|pages = 905–940|year = 1982|bibcode = 1982IJTP...21..905B|url = http://hexagon.physics.wisc.edu/teaching/2014f+ph805+quantum+information/papers/bennett+thermodynamics+of+computation+ijtp+1982.pdf|type = Submitted manuscript|citeseerx = 10.1.1.655.5610|s2cid = 17471991|access-date = 2017-12-10|archive-url = https://web.archive.org/web/20141014151011/http://hexagon.physics.wisc.edu/teaching/2014f%20ph805%20quantum%20information/papers/bennett%20thermodynamics%20of%20computation%20ijtp%201982.pdf|archive-date = 2014-10-14|url-status = dead}}</ref> Erasing information is a thermodynamically irreversible process that increases the entropy of a system. Although Bennett had reached the same conclusion as Szilard's 1929 paper, that a Maxwellian demon could not violate the second law because entropy would be created, he had reached it for different reasons.  Regarding [[Landauer's principle]], the minimum energy dissipated by deleting information was experimentally measured by Eric Lutz ''et al.'' in 2012. Furthermore, Lutz ''et al.'' confirmed that in order to approach the Landauer's limit, the system must asymptotically approach zero processing speed.<ref name="yFOHN">{{cite journal|doi=10.1038/nature.2012.10186|title=The unavoidable cost of computation revealed|journal=Nature|year=2012|last1=Ball|first1=Philip|s2cid=2092541}}</ref>
Recently, [[Landauer's principle]] has also been invoked to resolve an apparently unrelated paradox of statistical physics, [[Loschmidt’s paradox]]. <ref>{{cite journal|title=The reversibility paradox: Role of the velocity reversal step|author-last=Binder|author-first=P.M.|author-link=P.M. Binder|journal=[[International Journal of Theoretical Physics]]|date=2023|volume=62|issue=9 | page=200|doi=10.1007/s10773-023-05458-x |bibcode=2023IJTP...62..200B |url= https://rdcu.be/dmmuZ |doi-access=free}}</ref> 

[[John Earman]] and [[John D. Norton]] have argued that Szilárd and Landauer's explanations of Maxwell's demon begin by assuming that the [[second law of thermodynamics]] cannot be violated by the demon, and derive further properties of the demon from this assumption, including the necessity of consuming energy when erasing information, etc.<ref name="PAQSZ">{{cite journal|first1=John|last1=Earman|first2=John D.|last2=Norton|name-list-style=amp|year=1998|title=Exorcist XIV: The Wrath of Maxwell's Demon. Part I. From Maxwell to Szilard|url=http://www.pitt.edu/~jdnorton/papers/ExorcistXIV/Exorcist1.pdf|journal=Studies in History and Philosophy of Modern Physics|pages=435|volume=29|issue=4|doi=10.1016/s1355-2198(98)00023-9|bibcode=1998SHPMP..29..435E}}</ref><ref name="CyjZT">{{cite journal|first1=John|last1=Earman|first2=John D.|last2=Norton|name-list-style=amp|year=1999|title=Exorcist XIV: The Wrath of Maxwell's Demon. Part II. From Szilard to Landauer and Beyond|url=http://www.pitt.edu/~jdnorton/papers/ExorcistXIV/Exorcist2.pdf|journal=Studies in History and Philosophy of Modern Physics|pages=1|volume=30|issue=1|doi=10.1016/s1355-2198(98)00026-4|bibcode=1999SHPMP..30....1E}}</ref> It would therefore be circular to invoke these derived properties to defend the second law from the demonic argument. Bennett later acknowledged the validity of Earman and Norton's argument, while maintaining that [[Landauer's principle]] explains the mechanism by which real systems do not violate the second law of thermodynamics.<ref name="a5o0j">{{cite journal|first=Charles H.|last=Bennett|year=2002–2003|title=Notes on Landauer's principle, reversible computation, and Maxwell's demon|journal=Studies in History and Philosophy of Modern Physics|volume=34|issue=3|pages=501–510|arxiv=physics/0210005|bibcode = 2003SHPMP..34..501B|doi=10.1016/S1355-2198(03)00039-X|s2cid=9648186}}</ref>