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We propose a stochastic lattice gas model to describe the dynamics of two animal species population, one being a predator and the other a prey. This model comprehends the mechanisms of the Lotka-Volterra model. Our analysis was performed by using a dynamical mean-field approximation and computer simulations. Our results show that the system exhibits an oscillatory behavior of the population densities of prey and predators. For the sets of parameters used in our computer simulations, these oscillations occur at a local level. Mean-field results predict synchronized collective oscillations. 02.50.Ga,05.70.Ln Typeset using REVT E X

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

We study the entropy production in nonequilibrium systems described by a Fokker-Planck equation. We have devised an expression for the entropy flux in the stationary state. We have found that the entropy flux can be written as an ensemble average of an expression containing the force and its derivative. This result is similar to the one used by Lebowitz and Spohn for system following a Markovian process in discrete space. We have also been able to obtain a fluctuation-dissipation type relation between the dissipated power, which was written as an ensemble average, and the production of entropy for the case of systems in contact with one heat bath. We have applied the results for a simple model for particles subjected to dissipative forces.

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