Non-equilibrium relaxation process of complex systems and its statistical physical properties

TL;DR

This paper introduces a global iterative model for non-equilibrium complex systems that captures anomalous diffusion, non-Gaussian distributions, and long-term memory, based on data-driven coefficients.

Contribution

It presents a novel, data-driven model that describes the relaxation process of complex systems from non-equilibrium to equilibrium, capturing multiple time scale properties.

Findings

Model accurately represents anomalous diffusion phenomena.

Captures non-Gaussian distribution behaviors.

Exhibits long-term memory effects in complex systems.

Abstract

We constructed a model that evolved from a non-equilibrium state to an equilibrium state. The model only needs two basic coefficients, including self-similar coefficients and non-equilibrium coefficients. The coefficients of the model can be obtained directly from real data. The model can well represent the phenomena of anomalous diffusion, non-Gaussian distribution and so on in non-equilibrium complex systems. It is important to mention that the model is a global iterative model that can exhibit statistical physical properties on multiple time scales, as well as exhibiting long-term memory properties. This model may be used as a basic model for the research of various non-equilibrium relaxation process phenomena.