{"paper":{"title":"Relaxation Times for Nonextensive Systems Using Gradient Flow for the Maximization of Tsallis Entropy: An Application to Financial Market Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.MF","authors_text":"Sandhya Devi","submitted_at":"2026-06-22T19:16:49Z","abstract_excerpt":"In this work, we develop a method to estimate the relaxation time (the time required to reach equilibrium) of a nonextensive system such as financial market dynamics, using a Euclidean Gradient Flow (EGF) framework for the maximization of Tsallis entropy. The equilibrium state is defined as the maximum-entropy state. Specifically, the dynamics are expressed in terms of the time variations of the q-Gaussian parameters -- the entropic index q and the inverse temperature beta -- under the constraint that the distributions remain q-Gaussian at all times. We show that, for nonextensive systems, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23873","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23873/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}