Nonextensivity of the cyclic Lattice Lotka Volterra model

TL;DR

This paper demonstrates that the cyclic Lattice Lotka-Volterra model exhibits nonextensive entropy production with specific q-values, linked to fractal domain structures, revealing nonextensivity in a conservative many-body system.

Contribution

It provides the first numerical evidence of nonextensivity in a conservative many-body system through lattice simulations of the Lotka-Volterra model.

Findings

Finite entropy production at specific q-values for different growth modes.

Emergence of fractal boundaries in local particle domains.

Evidence of nonextensivity in a mean-field conservative system.

Abstract

We numerically show that the Lattice Lotka-Volterra model, when realized on a square lattice support, gives rise to a {\it finite} production, per unit time, of the nonextensive entropy $S_q= \frac{1- \sum_ip_i^q}{q-1}$ $(S_1=-\sum_i p_i \ln p_i)$. This finiteness only occurs for $q=0.5$ for the $d=2$ growth mode (growing droplet), and for $q=0$ for the $d=1$ one (growing stripe). This strong evidence of nonextensivity is consistent with the spontaneous emergence of local domains of identical particles with fractal boundaries and competing interactions. Such direct evidence is for the first time exhibited for a many-body system which, at the mean field level, is conservative.