Editing Maxwell's demon (section)

== Recent progress ==
Although the argument by Landauer and Bennett only answers the consistency between the second law of thermodynamics and the whole cyclic process of the entire system of a [[Entropy in thermodynamics and information theory#Szilard's engine|Szilard engine]] (a composite system of the engine and the demon), a recent approach based on the [[non-equilibrium thermodynamics]] for small fluctuating systems has provided deeper insight on each information process with each subsystem. From this viewpoint, the measurement process is regarded as a process where the correlation ([[mutual information]]) between the engine and the demon increases, decreasing the entropy of the system in an amount given by the mutual information.<ref name=":0">{{Cite journal|last1=Cao|first1=F. J.|last2=Feito|first2=M.|date=2009-04-10|title=Thermodynamics of feedback controlled systems|url=https://link.aps.org/doi/10.1103/PhysRevE.79.041118|journal=Physical Review E|language=en|volume=79|issue=4|page=041118 |doi=10.1103/PhysRevE.79.041118|pmid=19518184 |issn=1539-3755|arxiv=0805.4824|bibcode=2009PhRvE..79d1118C }}</ref> If the correlation changes, thermodynamic relations such as the second law of thermodynamics and the [[fluctuation theorem]] for each subsystem should be modified, and for the case of external control a second-law like inequality<ref name=":0" /><ref>{{Cite journal|last1=Sagawa|first1=Takahiro|last2=Ueda|first2=Masahito|date=2008-02-26|title=Second Law of Thermodynamics with Discrete Quantum Feedback Control|url=https://link.aps.org/doi/10.1103/PhysRevLett.100.080403|journal=Physical Review Letters|volume=100|issue=8|pages=080403|arxiv=0710.0956|bibcode=2008PhRvL.100h0403S|doi=10.1103/PhysRevLett.100.080403|pmid=18352605|s2cid=41799543}}</ref><ref name="HnKlB">{{cite journal|author1=Hugo Touchette|author2=Seth Lloyd|name-list-style=amp|year=2000|title=Information-Theoretic Limits of Control|journal=Physical Review Letters|volume=84|issue=6|pages=1156–1159|doi=10.1103/PhysRevLett.84.1156|bibcode = 2000PhRvL..84.1156T|pmid=11017467|arxiv=chao-dyn/9905039|s2cid=25507688}}</ref> and a generalized fluctuation theorem<ref name="GWNNE">{{cite journal|author1=Takahiro Sagawa|author2=Masahito Ueda|name-list-style=amp|year=2010|title=Generalized Jarzynski Equality under Nonequilibrium Feedback Control|journal=Physical Review Letters|volume=104|issue=9|pages=090602|doi=10.1103/PhysRevLett.104.090602|pmid=20366975|arxiv = 0907.4914|bibcode = 2010PhRvL.104i0602S|s2cid=1549122}}</ref> with mutual information are satisfied. For more general information processes including biological information processing, both inequality<ref name="HKXgx">{{cite journal|author=Armen E Allahverdyan, Dominik Janzing and Guenter Mahler|year=2009|title=Thermodynamic efficiency of information and heat flow|journal=Journal of Statistical Mechanics: Theory and Experiment|volume=2009|issue=9|pages=P09011|doi=10.1088/1742-5468/2009/09/P09011|arxiv = 0907.3320|bibcode = 2009JSMTE..09..011A|s2cid=118440998}}</ref> and equality<ref name="0VCnm">{{cite journal|author1=Naoto Shiraishi|author2=Takahiro Sagawa|name-list-style=amp|year=2015|title=Fluctuation theorem for partially masked nonequilibrium dynamics|journal=Physical Review E|volume=91|issue=1|pages=012130|doi=10.1103/PhysRevE.91.012130|pmid=25679593|arxiv = 1403.4018|bibcode = 2015PhRvE..91a2130S|s2cid=1805888}}</ref> with mutual information hold. When repeated measurements are performed, the entropy reduction of the system is given by the [[Entropy (information theory)#Entropy of a sequence|entropy of the sequence]] of measurements,<ref name=":0" /><ref>{{Cite journal|last1=Jarillo|first1=Javier|last2=Tangarife|first2=Tomás|last3=Cao|first3=Francisco J.|date=2016-01-22|title=Efficiency at maximum power of a discrete feedback ratchet|url=https://link.aps.org/doi/10.1103/PhysRevE.93.012142|journal=Physical Review E|volume=93|issue=1|pages=012142|doi=10.1103/PhysRevE.93.012142|pmid=26871058 |bibcode=2016PhRvE..93a2142J }}</ref><ref>{{Cite journal|last1=Ruiz-Pino|first1=Natalia|last2=Villarrubia-Moreno|first2=Daniel|last3=Prados|first3=Antonio|last4=Cao-García|first4=Francisco J.|date=2023-09-12|title=Information in feedback ratchets|url=https://link.aps.org/doi/10.1103/PhysRevE.108.034112|journal=Physical Review E|volume=108|issue=3|pages=034112|doi=10.1103/PhysRevE.108.034112|pmid=37849167 |arxiv=2303.16804 |bibcode=2023PhRvE.108c4112R |hdl=11441/161971 }}</ref> which takes into account the reduction of information due to the correlation between the measurements. More recently, Kastner has argued that the uncertainty principle forces an entropy increase when the molecule is localized to one side or the other in the Szilard engine, and that is what prevents the demon from violating the second law.<ref>{{Citation |last=Kastner |first=R. E. |title=Maxwell's Demon Is Foiled by the Entropy Cost of Measurement, Not Erasure |date=2025-03-23 |url=https://arxiv.org/abs/2503.18186 |access-date=2025-03-25 |arxiv=2503.18186 }}</ref> For the case of the original Demon who is sorting molecules by speeds, Kastner and Schlatter argue that the uncertainty principle prevents the Demon from sorting the molecules due to their delocalization upon measurement of momentum.<ref>{{Cite journal |last1=Kastner |first1=Ruth E. |last2=Schlatter |first2=Andreas |date=2024-01-08 |title=Entropy Cost of 'Erasure' in Physically Irreversible Processes |journal=Mathematics |language=en |volume=12 |issue=2 |pages=206 |doi=10.3390/math12020206 |doi-access=free |issn=2227-7390 |arxiv=2307.02643 }}</ref>