Entropy production in the cyclic lattice Lotka-Volterra model

Details Entropy production in the cyclic lattice Lotka-Volterra model Entropy production in the cyclic lattice Lotka-Volterra model

2004-02-09

arxiv.org/abs/cond-mat/0402248v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 6 figures

Scientific paper

10.1140/epjb/e2004-00379-2

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.

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