{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:17:14Z","timestamp":1760149034942,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T00:00:00Z","timestamp":1687910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Kazan Federal University Strategic Academic Leadership Program","award":["PRIORITY-2030"],"award-info":[{"award-number":["PRIORITY-2030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems\/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green\u2019s function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears.<\/jats:p>","DOI":"10.3390\/e25070989","type":"journal-article","created":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T01:53:57Z","timestamp":1688003637000},"page":"989","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Aftershocks and Fluctuating Diffusivity"],"prefix":"10.3390","volume":"25","author":[{"given":"Sumiyoshi","family":"Abe","sequence":"first","affiliation":[{"name":"Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China"},{"name":"Institute of Physics, Kazan Federal University, Kazan 420008, Russia"},{"name":"Department of Natural and Mathematical Sciences, Turin Polytechnic University in Tashkent, Tashkent 100095, Uzbekistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Norikazu","family":"Suzuki","sequence":"additional","affiliation":[{"name":"College of Science and Technology, Nihon University, Chiba 274-8501, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6106-7581","authenticated-orcid":false,"given":"Dmitrii A.","family":"Tayurskii","sequence":"additional","affiliation":[{"name":"Institute of Physics, Kazan Federal University, Kazan 420008, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Christensen, R.M. 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