ZhETF, Vol. 130,
p. 715 (October 2006)
(English translation - JETP,
Vol. 103, No. 4,
available online at www.springer.com
ENTROPY, FREE ENERGY AND PHASE TRANSITIONS IN THE LATTICE LOTKA - VOLTERRA MODEL
Chichigina O., Tsekouras G.A., Provata A.
Received: July 18, 2005
PACS: 82.60.-s, 05.45.Df, 82.65.+r
A thermodynamic approach is developed for reactive dynamic models restricted to substrates of arbitrary dimensions, including fractal substrates. The thermodynamic formalism is successfully applied to the lattice Lotka - Volterra (LLV) model of autocatalytic reactions on various lattice substrates. Different regimes of reactions described as phases, and phase transitions are obtained using this approach. Predictions of the thermodynamic theory confirm extensive numerical kinetic Monte Carlo simulations on square and fractal lattices. Extensions of the formalism to multispecies LLV models are also presented.