Entropy production in the cyclic lattice Lotka-Volterra model

TL;DR

This paper investigates entropy production in a cyclic lattice Lotka-Volterra model, showing that the entropy rate is finite and linear for a specific Tsallis entropy index related to the lattice dimension.

Contribution

It introduces a novel analysis of entropy growth in the lattice Lotka-Volterra model using Tsallis entropy, identifying a critical index linked to the system's dimension.

Findings

Entropy increases linearly over time at a specific Tsallis index.

The critical entropic index is $q_c=1-1/D$, related to lattice dimension.

Fractal patterns emerge despite simple entropy dynamics.

Abstract

The cyclic Lotka-Volterra model in a $D$-dimensional regular lattice is considered. Its ``nucleus growth'' mode is analyzed under the scope of Tsallis' entropies $S_q=(1-\sum_i p_i^q)/(q-1)$, $q\in \mathbb{R}$. It is shown both numerically and by means of analytical considerations that a linear increase of entropy with time, meaning finite asymptotic entropy rate, is achieved for the entropic index $q_c=1-1/D$. Although the lattice exhibits fractal patterns along its evolution, the characteristic value of $q$ can be interpreted in terms of very simple features of the dynamics.