Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems
arXiv:1406.6370 · doi:10.1209/0295-5075/110/10006
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.
References in corpus (35)
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- Langevin Equation for the Density of a System of Interacting Langevin Processes
- Dynamic first-order phase transition in kinetically constrained models of glasses
- Macroscopic fluctuation theory for stationary non equilibrium states
- Current fluctuations in non-equilibrium diffusive systems: an additivity principle
- Fluctuations in Stationary non Equilibrium States
- Macroscopic current fluctuations in stochastic lattice gases
- Space-time Thermodynamics of the Glass Transition
- Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries
- Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
- Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
- Probing rare physical trajectories with Lyapunov weighted dynamics
- Spontaneous Symmetry Breaking at the Fluctuating Level
- Mapping out of equilibrium into equilibrium in one-dimensional transport models
- Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
- Large deviations for a stochastic model of heat flow
- Hyperbolicity and the effective dimension of spatially-extended dissipative systems
- Concentration for One and Two Species One-Dimensional Reaction-Diffusion Systems
- Constrained dynamics of localized excitations causes a non-equilibrium phase transition in an atomistic model of glass formers
- Microscopic chaos from Brownian motion?
- Dynamic transition in an atomic glass former: a molecular dynamics evidence
- Extreme Current Fluctuations in Lattice Gases: Beyond Nonequilibrium Steady States
- Equilibrium-like fluctuations in some boundary-driven open diffusive systems
- Current fluctuations in systems with diffusive dynamics, in and out of equilibrium
- Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations
- Vortex-density fluctuations, energy spectra and vortical regions in superfluid turbulence
- Dynamical phase transitions in supercooled liquids: interpreting measurements of dynamical activity
- Nonconcave entropies in multifractals and the thermodynamic formalism
- A large-deviation approach to space-time chaos
- Collective Lyapunov modes
- Universal scaling of Lyapunov-exponent fluctuations in space-time chaos
- Fluctuations of the heat flux of a one-dimensional hard particle gas
- Damage spreading and dynamic stability of kinetic Ising models
- Large deviations and heterogeneities in a driven kinetically constrained model
- Thermodynamic formalism and localization in Lorentz gases and hopping models