Extreme Current Fluctuations in Lattice Gases: Beyond Nonequilibrium Steady States

Abstract

We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in non-stationary diffusive lattice gases. We identify two universality classes of these fluctuations which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of \emph{effective fluid}, obtained by mapping the MFT into an inviscid hydrodynamics. An example of the elliptic class is the Symmetric Simple Exclusion Process where, for some initial conditions, we can solve the effective hydrodynamics exactly. This leads to a super-Gaussian extreme current statistics conjectured by Derrida and Gerschenfeld (2009) and yields the optimal path of the system. For models of the hyperbolic class the deterministic mass flux cannot be neglected, leading to a different extreme current statistics.

6 pages (including Supplemental Material), 3 figures

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Cited by in corpus (29)

• Macroscopic fluctuation theory
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation
• Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
• Short-time height distribution in 1d KPZ equation: starting from a parabola
• Dynamical phase transitions in the current distribution of driven diffusive channels
• Survival of a static target in a gas of diffusing particles with exclusion
• 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
• Finite-size effects in the short-time height distribution of the Kardar-Parisi-Zhang equation
• Weak additivity principle for current statistics in d-dimensions
• Survival of interacting diffusing particles inside a domain with absorbing boundary
• Extreme Fluctuations of Current in the Symmetric Simple Exclusion Process: a Non-Stationary Setting
• The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles
• Large fluctuations in diffusion-controlled absorption
• The kinetic exclusion process: a tale of two fields
• Macroscopic fluctuation theory and first-passage properties of surface diffusion
• Melting of an Ising Quadrant
• Extreme current fluctuations of boundary-driven systems in the large-N limit
• Macroscopic fluctuation theory of local time in lattice gases
• 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
• Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems
• Emptiness Formation in Polytropic Quantum Liquids
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Inverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model
• Structure of the optimal path to a fluctuation
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions