Nonequilibrium Fluctuations in a Gaussian Galton Board (or Periodic Lorentz Gas) Using Long Periodic Orbits

TL;DR

This paper investigates nonequilibrium fluctuations in a Gaussian Galton Board model by analyzing extremely long periodic orbits, providing insights into fluctuation theorems and distribution functions in complex dynamical systems.

Contribution

It introduces a detailed analysis of long periodic orbits in a Gaussian Galton Board, linking fluctuation theorems to fractal nonequilibrium distributions.

Findings

Verification of fluctuation theorems in a complex dynamical system

Analysis of extremely long periodic orbits with billions of collisions

Insights into nonequilibrium distribution functions

Abstract

Predicting nonequilibrium fluctuations requires a knowledge of nonequilibrium distribution functions. Despite the distributions' fractal character some theoretical results, "Fluctuation Theorems", reminiscent of but distinct from, Gibbs' equilibrium statistical mechanics and the Central Limit Theorem, have been established away from equilibrium and applied to simple models. We summarize the simplest of these results for a Gaussian-thermostated Galton Board problem, a field-driven mass point moving through a periodic array of hard-disk scatterers. The billion-collision trillion-timestep data we analyze correspond to periodic orbits with up to 793,951,594 collisions and 447,064,397,614 timesteps.