The nonequilibrium Ehrenfest gas: a chaotic model with flat obstacles?

TL;DR

This paper investigates the non-equilibrium Ehrenfest gas, revealing it can exhibit both chaotic and non-chaotic steady states with highly irregular transport behavior, influenced by field and geometry, challenging previous assumptions about similar models.

Contribution

The study provides the first analytical and numerical evidence that the non-equilibrium Ehrenfest gas can have both chaotic and non-chaotic steady states, despite its non-dispersing rhombic obstacles.

Findings

Supports existence of both chaotic and non-chaotic steady states

Shows transport behavior is highly irregular and sensitive to parameters

Reveals new phenomena not observed in similar models

Abstract

It is known that the non-equilibrium version of the Lorentz gas (a billiard with dispersing obstacles, electric field and Gaussian thermostat) is hyperbolic if the field is small. Differently the hyperbolicity of the non-equilibrium Ehrenfest gas constitutes an open problem, since its obstacles are rhombi and the techniques so far developed rely on the dispersing nature of the obstacles. We have developed analytical and numerical investigations which support the idea that this model of transport of matter has both chaotic (positive Lyapunov exponent) and non-chaotic steady states with a quite peculiar sensitive dependence on the field and on the geometry, not observed before. The associated transport behaviour is correspondingly highly irregular, with features whose understanding is of both theoretical and technological interest.