[en] We introduce and analyze numerically a nonequilibrium model with a conserved dynamics which is a realization of the contact process in an ensemble of constant particle number. The model possesses just one process in which particles jump around landing only on empty sites next to an existing particle. Particles are not allowed to land on a vacant site surrounded by empty sites. In contrast with the ordinary contact process, the present model does not have an absorbing state. In spite of lacking an absorbing state, the model displays properties that, in the thermodynamic limit, are identical to those of the ordinary contact process

[en] An out of equilibrium Glauber–Ising model, evolving in accordance with an irreversible and stochastic Markovian dynamics, is analyzed in order to improve our comprehension concerning critical behavior and phase transitions in nonequilibrium systems. Therefore, a lattice model ruled by the competition between two Glauber dynamics acting on interlaced square lattices is proposed. Previous results have shown how the entropy production provides information about irreversibility and criticality. Mean-field approximations and Monte Carlo simulations were used in the analysis. The results obtained here show a continuous phase transition, reflected in the entropy production as a logarithmic divergence of its derivative, which suggests a shared universality class with the irreversible models invariant under the symmetry operations of the Ising model. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

[en] The critical behavior of the entropy production rate is analyzed for lattice models defined to be invariant under transformations comprising the symmetry group , and irreversible dynamically as well. A stochastic approach is followed, considering Markovian processes in continuous time, and therefore assuming a master equation representation for the time evolution of the probability distribution of states. The quantitative analysis is mostly supported by results from Monte Carlo simulations, which revealed a divergent behavior in the derivative of the entropy production at the critical point. This divergence is characterized by the critical exponent , in close analogy with the critical behavior of the specific heat of the three-state Potts model, supporting with it the conjecture stating that the class of universality of a system is not directly affected by its reversibility conditions. (paper)

[en] We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and covariances of the random variables in question. These include the total rate of change of the entropy, the entropy production rate, the entropy flux rate and the three components of the entropy production. All equations are cast in a way suitable for large-scale analysis of linear Langevin systems. Our results are also applied to different types of electrical circuits, which suitably illustrate the most relevant aspects of the problem. (paper)

[en] We analyse a method to determine the short-time exponent θ related to the critical initial slip in stochastic lattice models. In this method it suffices to start with an uncorrelated state with a vanishing order parameter instead of departing, as is usually done, from an initial state with a nonvanishing order parameter. The exponent θ is calculated by the time correlation of the order parameter. This method, deduced previously for up-down symmetry models, is extended here to include models with other symmetries. We also consider the extension to cover models with absorbing states

[en] We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka-Volterra model. Two levels of mean-field approximations are set up. The simple approximation is equivalent to an extended patch model, a simple metapopulation model with patches colonized by prey, patches colonized by predators and empty patches. This approximation is capable of describing the limited available space for species occupancy. The pair approximation is moreover able to describe two types of coexistence of prey and predators: one where population densities are constant in time and another displaying self-sustained time oscillations of the population densities. The oscillations are associated with limit cycles and arise through a Hopf bifurcation. They are stable against changes in the initial conditions and, in this sense, they differ from the Lotka-Volterra cycles which depend on initial conditions. In this respect, the present model is biologically more realistic than the Lotka-Volterra model

[en] We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out mean-field approximations and numerical simulations we obtain the phase boundaries (thresholds) related to the transition between an active state, where prey and predators present a stable coexistence, and a prey absorbing state. The numerical estimates for the critical exponents show that the transition belongs to the directed percolation universality class. In the limit where the cellular automaton maps into a model for the spreading of an epidemic with immunization we observe a crossover from directed percolation class to the dynamic percolation class. Patterns of growing clusters related to species coexistence and spreading of epidemic are shown and discussed

[en] The critical properties of the stochastic susceptible-exposed-infected model on a square lattice is studied by numerical simulations and by the use of scaling relations. In the presence of an infected individual, a susceptible becomes either infected or exposed. Once infected or exposed, the individual remains forever in this state. The stationary properties are shown to be the same as those of isotropic percolation so that the critical behavior puts the model into the universality class of dynamic percolation. (paper)

[en] Two stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the disease in the former is found to occur when the infection probability b is larger than b_c = k/2(k - 1). In the latter, which is equivalent to a dynamic site percolation model, the spreading occurs when the infection probability p is greater than p_c = 1/(k - 1). We set up and solve the time evolution equations for both models and determine the final and time-dependent properties, including the epidemic curve. We show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p = b/[k - (k - 1)b]. These include the cluster size distribution and the density of individuals of each type, quantities that have been determined in closed forms.

[en] The critical behaviour of two-dimensional stochastic lattice gas models with C_3v symmetry is analysed. We study the cumulants of the order parameter for the three-state (equilibrium) Potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group C_3v. By means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behaviour of the systems. In particular, we find that the Binder reduced fourth-order cumulant takes a universal value U* which is the same for the three-state Potts model and for the irreversible models. The same universal behaviour is observed for the reduced third-order cumulant. (author)