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

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.