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This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a unified picture is emerging at the macroscopic level, applicable, in our view, to real phenomena where diffusion is the dominating physical mechanism. We rely mainly on an approach developed by the authors based on the study of dynamical large fluctuations in stationary states of open systems. The outcome of this approach is a theory connecting the non equilibrium thermodynamics to the transport coefficients via a variational principle. This leads ultimately to a functional derivative equation of Hamilton-Jacobi type for the non equilibrium free energy in which local thermodynamic variables are the independent arguments. In the first part of the paper we give a detailed introduction to the microscopic dynamics considered, while the second part, devoted to the macroscopic properties, illustrates many consequences of the Hamilton-Jacobi equation. In both parts several novelties are included.
Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSSs) whose lifetime increases with system size. The application of Lynden-Bells theory of violent relaxation to the Hamiltonian Mean Field model le
One particle in a classical perfect gas is driven out of equilibrium by changing its mass over a short time interval. The work done on the driven particle depends on its collisions with the other particles in the gas. This model thus provides an exam
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take very long ti
In this review we present some of the work done in India in the area of driven and out-of-equilibrium systems with topological phases. After presenting some well-known examples of topological systems in one and two dimensions, we discuss the effects
We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large deviation prin