Extreme Current Fluctuations in a Nonstationary Stochastic Heat Flow

Abstract

We employ the Hamiltonian formalism of macroscopic fluctuation theory to study large deviations of integrated current in the Kipnis-Marchioro-Presutti (KMP) model of stochastic hear flow when starting from a step-like initial condition. The KMP model belongs to the hyperbolic universality class where diffusion remains relevant no matter how large the fluctuating current is. The extreme current statistics for the KMP model turns out to be sub-Gaussian, as distinguished from the super-Gaussian statistics found for the Symmetric Simple Exclusion Process and other models of the elliptic class. The most probable time history of the system, which dominates the extreme current statistics of the KMP model, involves two large-amplitude solitary pulses: of the energy density field and of the conjugate "momentum" field. The coupled pulses propagate with a constant speed, but their amplitudes slowly grow with time, as the energy density pulse collects most of the available energy on its way.

20 pages in preprint format, 7 figures

References in corpus (8)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
• Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models
• Inactive dynamical phase of a symmetric exclusion process on a ring
• Void formation in diffusive lattice gases

Cited by in corpus (21)

• Macroscopic fluctuation theory
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
• Dynamical phase transitions in the current distribution of driven diffusive channels
• Survival of a static target in a gas of diffusing particles with exclusion
• Extreme Current Fluctuations in Lattice Gases: Beyond Nonequilibrium Steady States
• Statistics of large currents in the Kipnis-Marchioro-Presutti model in a ring geometry
• Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case
• Survival of interacting diffusing particles inside a domain with absorbing boundary
• Weak additivity principle for current statistics in d-dimensions
• Extreme Fluctuations of Current in the Symmetric Simple Exclusion Process: a Non-Stationary Setting
• Large fluctuations in diffusion-controlled absorption
• The kinetic exclusion process: a tale of two fields
• Singularities in Large Deviation Functionals of Bulk-Driven Transport Models
• Solitons in fluctuating hydrodynamics of diffusive processes
• Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions
• Full absorption statistics of diffusing particles with exclusion
• Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions
• Full Statistics of Regularized Local Energy Density in a Freely Expanding Kipnis-Marchioro-Presutti Gas