Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems

TL;DR

This paper develops a formalism to compute the largest Lyapunov exponent and its fluctuations in diffusive systems, linking dynamical systems theory with non-equilibrium statistical mechanics, and validates it with simulations and models.

Contribution

It introduces a general analytical approach for Lyapunov exponents in diffusive hydrodynamics, extending dynamical systems concepts to non-equilibrium spatially extended systems.

Findings

Analytical results agree with lattice model simulations.

Formalism relates Lyapunov exponents to damage spreading and pair annihilation.

Provides new finite size results for the Symmetric Simple Exclusion Process.

Abstract

We present a general formalism for computing the largest Lyapunov exponent and its fluctuations in spatially extended systems described by diffusive fluctuating hydrodynamics, thus extending the concepts of dynamical system theory to a broad range of non-equilibrium systems. Our analytical results compare favourably with simulations of a lattice model of heat conduction. We further show how the computation of the Lyapunov exponent for the Symmetric Simple Exclusion Process relates to damage spreading and to a two-species pair annihilation process, for which our formalism yields new finite size results.