How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems

10922 7 61457 3 168953 document 61457 How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems.pdf application/pdf 7d00be04c8bcc663e9a488decc51076b MD5 702270 2016-06-09 12:48:37 https://pure.iiasa.ac.at/id/eprint/10922/1/How%20multiplicity%20determines%20entropy%20and%20the%20derivation%20of%20the%20maximum%20entropy%20principle%20for%20complex%20systems.pdf 10922 1 1 application/pdf text en public cc_by_nc

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems.pdf

published 61465 2 168967 document 61465 lightbox.jpg image/png d323bc8e432aa80ddc8883076f86e0c5 MD5 72595 2016-06-09 12:58:59 https://pure.iiasa.ac.at/id/eprint/10922/2/lightbox.jpg 10922 2 2 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/61457 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/61457 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/61457 archive 351 disk0/00/01/09/22 2016-01-15 08:50:44 2021-08-27 17:39:40 2016-01-15 08:50:44 article show Hanel R. Thurner S. 1918 Gell-Mann M. How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems pub iis_met iis_sys prog_asa Thermodynamics; Out-of-equilibrium process; Driven systems; Random walk The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process. 2014-05 published National Academy of Sciences 10.1073/pnas.1406071111 XJ-14-128 PNAS; 111(19):6905-6910 (13 May 2014) (Published online 29 April 2014) [doi:10.1073/pnas.1406071111] 307 public Proceedings of the National Academy of Sciences 111 19 6905-6910 TRUE 1091-6490 FALSE info:eu-repo/semantics/article