Diffusive Lorentz gases and multibaker maps are compatible with irreversible thermodynamics

Abstract

We show that simple diffusive systems, such as the Lorentz gas and multibaker maps are perfectly compatible with the laws of irreversible thermodynamics, despite the fact that the moving particles, or their equivalents, in these models do not interact with each other, and that the dynamics takes place in low-dimensional phase spaces. The interaction of moving particles with scatterers provides the dynamical mechanism responsible for an approach to equilibrium, under appropriate conditions. This analysis provides a refutation of the criticisms expressed recently by Cohen and Rondoni [Physica A 306 (2002) 117-128].

Heat conduction and Fourier's law in a class of many particle dispersing billiards

“…Here, rather than local thermal equilibrium, it is a relaxation to local equilibrium, occurring on the constant energy sheet of the individual tracer particles, which allows to model the mass transport by a random walk and yields an analytic estimate of the diffusion coefficient [5]. Arguably Lorentz gases, whether periodic or disordered, in or out of equilibrium, have played, over more than a century, a privileged and most important role in the development of transport and kinetic theories [6]. However, in the absence of interaction among the tracer particles, there is no mechanism for energy exchange and therefore no process of thermalization before heat is conducted.…”

Initial growth of Boltzmann entropy and chaos in a large assembly of weakly interacting systems

“…These issues are the source of heated debates, on which only partial agreement has been reached within the statistical mechanics community. Recent examples of this are given by the debate on irreversibility originated by Lebowitz's paper [4], and the partly contrasting views on irreversible entropy production reported in [12,13,14,15].…”

General self-similar solutions of diffusion equation and related constructions

“…Connections with non-equilibrium thermodynamics were analyzed in [20], and [21]. Beyond diffusion Mátyás and Gaspard [22] discussed diffusion with a simple reaction -isomerization -where not only the diffusion coefficient, but the reaction rate is also evaluated.…”