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Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-23835
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dc.contributor.authorSchmidhuber, Christoph-
dc.date.accessioned2022-01-07T11:28:07Z-
dc.date.available2022-01-07T11:28:07Z-
dc.date.issued2021-10-01-
dc.identifier.issn0378-4371de_CH
dc.identifier.issn1873-2119de_CH
dc.identifier.urihttps://digitalcollection.zhaw.ch/handle/11475/23835-
dc.description.abstractWe consider the statistical mechanical ensemble of bit string histories that are computed by a universal Turing machine. The role of the energy is played by the program size. We show that this ensemble has a first-order phase transition at a critical temperature, at which the partition function equals Chaitin’s halting probability Ω. This phase transition has curious properties: the free energy is continuous near the critical temperature, but almost jumps: it converges more slowly to its finite critical value than any computable function. At the critical temperature, the average size of the bit strings diverges. We define a non-universal Turing machine that approximates this behavior of the partition function in a computable way by a super-logarithmic singularity, and discuss its thermodynamic properties. We also discuss analogies and differences between Chaitin’s Omega and the partition function of a quantum mechanical particle, and with quantum Turing machines. For universal Turing machines, we conjecture that the ensemble of bit string histories at the critical temperature has a continuum formulation in terms of a string theory.de_CH
dc.language.isoende_CH
dc.publisherElsevierde_CH
dc.relation.ispartofPhysica A: Statistical Mechanics and its Applicationsde_CH
dc.rightshttp://creativecommons.org/licenses/by/4.0/de_CH
dc.subjectChaitin's Omegade_CH
dc.subjectTuring machinede_CH
dc.subjectComplexityde_CH
dc.subjectAlgorithmic thermodynamicsde_CH
dc.subject.ddc510: Mathematikde_CH
dc.titleChaitin’s Omega and an algorithmic phase transitionde_CH
dc.typeBeitrag in wissenschaftlicher Zeitschriftde_CH
dcterms.typeTextde_CH
zhaw.departementSchool of Engineeringde_CH
zhaw.organisationalunitInstitut für Datenanalyse und Prozessdesign (IDP)de_CH
dc.identifier.doi10.1016/j.physa.2021.126458de_CH
dc.identifier.doi10.21256/zhaw-23835-
zhaw.funding.euNode_CH
zhaw.originated.zhawYesde_CH
zhaw.pages.start126458de_CH
zhaw.publication.statuspublishedVersionde_CH
zhaw.volume586de_CH
zhaw.publication.reviewPeer review (Publikation)de_CH
zhaw.webfeedInformation Engineeringde_CH
zhaw.author.additionalNode_CH
zhaw.display.portraitYesde_CH
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Schmidhuber, C. (2021). Chaitin’s Omega and an algorithmic phase transition. Physica A: Statistical Mechanics and Its Applications, 586, 126458. https://doi.org/10.1016/j.physa.2021.126458
Schmidhuber, C. (2021) ‘Chaitin’s Omega and an algorithmic phase transition’, Physica A: Statistical Mechanics and its Applications, 586, p. 126458. Available at: https://doi.org/10.1016/j.physa.2021.126458.
C. Schmidhuber, “Chaitin’s Omega and an algorithmic phase transition,” Physica A: Statistical Mechanics and its Applications, vol. 586, p. 126458, Oct. 2021, doi: 10.1016/j.physa.2021.126458.
SCHMIDHUBER, Christoph, 2021. Chaitin’s Omega and an algorithmic phase transition. Physica A: Statistical Mechanics and its Applications. 1 Oktober 2021. Bd. 586, S. 126458. DOI 10.1016/j.physa.2021.126458
Schmidhuber, Christoph. 2021. “Chaitin’s Omega and an Algorithmic Phase Transition.” Physica A: Statistical Mechanics and Its Applications 586 (October): 126458. https://doi.org/10.1016/j.physa.2021.126458.
Schmidhuber, Christoph. “Chaitin’s Omega and an Algorithmic Phase Transition.” Physica A: Statistical Mechanics and Its Applications, vol. 586, Oct. 2021, p. 126458, https://doi.org/10.1016/j.physa.2021.126458.


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