Relaxation Times for Nonextensive Systems Using Gradient Flow for the Maximization of Tsallis Entropy: An Application to Financial Market Dynamics

Sandhya Devi

Papers from arXiv.org

Abstract: 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 relaxation times are longer than those obtained from the maximization of Shannon entropy, indicating that predictions over longer times are possible.

Date: 2026-06
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