{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T14:49:05Z","timestamp":1773758945685,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2013,12,3]],"date-time":"2013-12-03T00:00:00Z","timestamp":1386028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2013Khinchin axioms and by violating the fourth, the so-called composition axiom. The corresponding entropy is of the form Sc,d ~ \u2211i\u0393(1 + d, 1 \u2212 cln pi) 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 \u201caging\u201d walks. These are systems whose transition rates between states are path- and time-dependent. We show that for particular aging walks, Sc,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.<\/jats:p>","DOI":"10.3390\/e15125324","type":"journal-article","created":{"date-parts":[[2013,12,3]],"date-time":"2013-12-03T11:15:30Z","timestamp":1386069330000},"page":"5324-5337","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Generalized (c,d)-Entropy and Aging Random Walks"],"prefix":"10.3390","volume":"15","author":[{"given":"Rudolf","family":"Hanel","sequence":"first","affiliation":[{"name":"Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, Vienna A-1090, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Thurner","sequence":"additional","affiliation":[{"name":"Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, Vienna A-1090, Austria"},{"name":"Santa Fe Institute,1399 Hyde Park Road, Santa Fe, NM87501, USA"},{"name":"Institute for Applied Systems Analysis, Schlossplatz 1, Laxenburg A-2361, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,12,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20006","DOI":"10.1209\/0295-5075\/93\/20006","article-title":"A comprehensive classification of complex statistical systems and an axiomatic derivation of their entropy and distribution functions","volume":"93","author":"Hanel","year":"2011","journal-title":"Europhys. 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