Some recent developments in models with absorbing states

We describe some of the recent results obtained for models with absorbing states. First, we present the nonequilibrium absorbing-state Potts model and discuss some of the factors that might affect the critical behaviour of such models. In particular we show that in two dimensions the further neighbour interactions might split the voter critical point into two critical points. We also describe some of the results obtained in the context of synchronization of chaotic dynamical systems. Moreover, we discuss the relation of the synchronization transition with some interfacial models.Comment: 8 pages, Brazilian J. of Physics (in press

Dependence of the fluctuation-dissipation temperature on the choice of observable

On general grounds, a nonequilibrium temperature can be consistently defined from generalized fluctuation-dissipation relations only if it is independent of the observable considered. We argue that the dependence on the choice of observable generically occurs when the phase-space probability distribution is non-uniform on constant energy shells. We relate quantitatively this observable dependence to a fundamental characteristics of nonequilibrium systems, namely the Shannon entropy difference with respect to the equilibrium state with the same energy. This relation is illustrated on a mean-field model in contact with two heat baths at different temperatures.Comment: 4 pages, 2 figures, final versio

Front formation in a ballistic annihilation model

We study a simple one-dimensional model of ballisticaly-controlled annihilation in which the two annihilating species are initially spatially separated. The time dependent properties of the annihilation front are exactly derived. It is shown that the front wanders in a brownian fashion around its average value.Comment: Typeset using Latex, with Elsevier macros (elsart); 17 pages with one Latex figure and two Encapsulated Postscript figures (need epsf

Competing Species Dynamics: Qualitative Advantage versus Geography

A simple cellular automata model for a two-group war over the same territory is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are instrumental to overcome a less fitted majority. The model applies to a large spectrum of competing groups: smoker-non smoker war, epidemic spreading, opinion formation, competition for industrial standards and species evolution. In the last case, it provides a new explanation for punctuated equilibria.Comment: 7 pages, latex, 2 figures include

Intensive thermodynamic parameters in nonequilibrium systems

Considering a broad class of steady-state nonequilibrium systems for which some additive quantities are conserved by the dynamics, we introduce from a statistical approach intensive thermodynamic parameters (ITPs) conjugated to the conserved quantities. This definition does not require any detailed balance relation to be fulfilled. Rather, the system has to satisfy a general additivity property, which holds in most of the models usually considered in the literature, including those described by a matrix product ansatz with finite matrices. The main property of these ITPs is to take equal values in two subsystems, making them a powerful tool to describe nonequilibrium phase coexistence, as illustrated on different models. We finally discuss the issue of the equalization of ITPs when two different systems are put into contact. This issue is closely related to the possibility of measuring the ITPs using a small auxiliary system, in the same way as temperature is measured with a thermometer, and points at one of the major difficulties of nonequilibrium statistical mechanics. In addition, an efficient alternative determination, based on the measure of fluctuations, is also proposed and illustrated.Comment: 17 pages, 5 figures; final version, with minor change