Volume 110, Number 1, April 2015
|Number of page(s)||6|
|Published online||23 April 2015|
Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems
1 Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France
2 Department of Mathematics, King's College London - Strand, London WC2R 2LS, UK
Received: 14 January 2015
Accepted: 1 April 2015
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.45.-a – Nonlinear dynamics and chaos / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EPLA, 2015
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