Fractality of the non-equilibrium stationary states of open volume-preserving systems: I. Tagged particle diffusion

TL;DR

This paper investigates the fractal nature of non-equilibrium stationary states in open, volume-preserving diffusive systems, linking their phase-space fractality to macroscopic thermodynamic properties like entropy production.

Contribution

It establishes a theoretical connection between the fractality of stationary states and thermodynamic diffusion processes in deterministic systems.

Findings

Fractal properties of stationary states are characterized and linked to macroscopic diffusion.

Entropy production rate is derived from first principles using Gaspard's formalism.

The study provides a framework for understanding phase-space statistics in non-equilibrium systems.

Abstract

Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker map, as well as spatially periodic systems of interacting particles, have non-equilibrium stationary states with fractal properties when put in contact with particle reservoirs at their boundaries. We study the macroscopic limits of these systems and establish a correspondence between the thermodynamics of the macroscopic diffusion process and the fractality of the stationary states that characterize the phase-space statistics. In particular the entropy production rate is recovered from first principles using a formalism due to Gaspard [J. Stat. Phys. 88, 1215 (1997)]. This article is the first of two; the second article considers the influence of a uniform external field on such systems.