Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile

2009/07/31 by Bernard Derrida, B. Derrida, Antoine Gerschenfeld +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Current (fluid) #Current density #Distribution (mathematics) #Initial value problem #Range (aeronautics) #Simple (philosophy) #Stochastic processes and statistical mechanics #Symmetry (geometry) #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1007/s10955-009-9830-1

17 pages, 2 figures

arxiv created 2009/09/10 · openalex publication_date 2009/09/24 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show how to apply the macroscopic fluctuation theory (MFT) of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim to study the current fluctuations of diffusive systems with a step initial condition. We argue that one has to distinguish between two ways of averaging (the annealed and the quenched cases) depending on whether we let the initial condition fluctuate or not. Although the initial condition is not a steady state, the distribution of the current satisfies a symmetry very reminiscent of the fluctuation theorem. We show how the equations of the MFT can be solved in the case of non-interacting particles. The symmetry of these equations can be used to deduce the distribution of the current for several other models, from its knowledge for the symmetric simple exclusion process. In the range where the integrated current Q_t ∼ √(t), we show that the non-Gaussian decay exp [- Q_t³/t] of the distribution of Q_t is generic.

Citations

• The Fluctuation Theorem as a Gibbs Property
• Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case
• Distribution of current in nonequilibrium diffusive systems and phase transitions
• Large Deviations for a Stochastic Model of Heat Flow
• Current fluctuations in the exclusion process and Bethe ansatz
• A Fredholm Determinant Representation in ASEP
• Current fluctuations in the zero-range process with open boundaries
• Strong Asymmetric Limit of the Quasi-Potential of the Boundary Driven Weakly Asymmetric Exclusion Process
• Universal cumulants of the current in diffusive systems on a ring
• Mapping out-of-equilibrium into equilibrium in one-dimensional transport models
• Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

Cited by

• Transport in quantum chains under strong monitoring
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation