Generalized (c,d)-entropy and aging random walks

10306 6 72130 2 199568 document 72130 Generalized (c,d)-Entropy and Aging Random Walks.pdf application/pdf 50516fe9f09335697d5553dd6e410727 MD5 485532 2016-10-25 12:46:12 https://pure.iiasa.ac.at/id/eprint/10306/1/Generalized%20%28c%2Cd%29-Entropy%20and%20Aging%20Random%20Walks.pdf 10306 1 1 application/pdf text en public cc_by

Generalized (c,d)-Entropy and Aging Random Walks.pdf

published 72131 2 199571 document 72131 lightbox.jpg image/png 59e3b76a03765b449b8c4d21163442ab MD5 45167 2016-10-25 12:46:35 https://pure.iiasa.ac.at/id/eprint/10306/2/lightbox.jpg 10306 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/72130 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/72130 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/72130 archive 351 disk0/00/01/03/06 2016-01-15 08:48:28 2021-08-27 17:39:23 2016-01-15 08:48:28 article show Hanel R. Thurner S. 1918 Generalized (c,d)-entropy and aging random walks pub iis_met iis_sys prog_asa Non-ergodic; Extensivity; Path-dependence; Random walks with memory Complex systems are often inherently non-ergodic and non-Markovian and Shannon entropy loses its applicability. Accelerating, path-dependent and aging random walks offer an intuitive picture for non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived from three of the Shannon-Khinchin axioms and by violating the fourth, the so-called composition axiom. The corresponding entropy is of the form S_c,d~Sum_i Gamma(1+d, 1-c ln p_i) and depends on two system-specific scaling exponents, c and d. This entropy contains many recently proposed entropy functionals as special cases, including Shannon and Tsallis entropy. It was shown that this entropy is relevant for a special class of non-Markovian random walks. In this work, we generalize these walks to a much wider class of stochastic systems that can be characterized as "aging" walks. These are systems whose transition rates between states are path- and time-dependent. We show that for particular aging walks, S_c,d is again the correct extensive entropy. Before the central part of the paper, we review the concept of (c,d)-entropy in a self-contained way. 2013-12 published Molecular Diversity Preservation International (MDPI) 10.3390/e15125324 XJ-13-241 Entropy; 15(12):5084-5596 (December 2013) (Published online 3 December 2013) [doi:10.3390/e15125324] 307 public Entropy 15 12 5084-5596 TRUE 1099-4300 FALSE info:eu-repo/semantics/article