Self-organization in nonadditive systems with external noise

TL;DR

This paper extends Klimontovich's S-theorem using Tsallis entropy to analyze self-organization in nonadditive systems with inverse power law distributions under external noise.

Contribution

It introduces a nonadditive generalization of S-theorem applicable to systems with power law stationary distributions, demonstrating self-organization.

Findings

Entropy decreases as the system moves away from equilibrium.

The nonadditivity index q is confined to the range (0.5,1].

Application to the modified Van der Pol oscillator shows self-organization.

Abstract

A nonadditive generalization of Klimontovich's S-theorem [G. B. Bagci, Int.J. Mod. Phys. B 22, 3381 (2008)] has recently been obtained by employing Tsallis entropy. This general version allows one to study physical systems whose stationary distributions are of the inverse power law in contrast to the original S-theorem, which only allows exponential stationary distributions. The nonadditive S-theorem has been applied to the modified Van der Pol oscillator with inverse power law stationary distribution. By using nonadditive S-theorem, it is shown that the entropy decreases as the system is driven out of equilibrium, indicating self-organization in the system. The allowed values of the nonadditivity index $q$ are found to be confined to the regime (0.5,1].