Nonextensivity of the cyclic Lattice Lotka Volterra model

Details Nonextensivity of the cyclic Lattice Lotka Volterra model Nonextensivity of the cyclic Lattice Lotka Volterra model

2003-03-06

arxiv.org/abs/cond-mat/0303104v1

Physics

Condensed Matter

Latex, 6 pages, 5 figures

Scientific paper

10.1103/PhysRevE.69.016120

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.

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