Non-differentiable large-deviation functionals in boundary-driven diffusive systems

Equilibriumlike fluctuations in some boundary-driven open diffusive systems.

There exist some boundary-driven open systems with diffusive dynamics whose particle current fluctuations exhibit universal features that belong to the Edwards-Wilkinson universality class. We achieve this result by establishing a mapping, for the system fluctuations, to an equivalent open yet equilibrium-diffusive system. We discuss the possibility of observing dynamic phase transitions using ...

On Differentiable Functionals

Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process

We consider the asymmetric exclusion process (ASEP) in one dimension on sites i = 1, ..., N , in contact at sites i = 1 and i = N with infinite particle reservoirs at densities ρa and ρb. As ρa and ρb are varied, the typical macroscopic steady state density profile ρ̄(x), x ∈ [a, b], obtained in the limit N = L(b − a) → ∞, exhibits shocks and phase transitions. Here we derive an exact asymptotic...

A perturbation theory for large deviation functionals in fluctuating hydrodynamics

We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the fluctuation theorem, we first relate the large deviation functional with a minimization problem. We then develop a perturbation method for solving the problem. I...

Boltzmann’s Entropy and Large Deviation Lyapunov Functionals for Closed and Open Macroscopic Systems

I give a brief overview of the resolution of the apparent problem of reconciling time symmetric microscopic dynamic with time asymmetric equations describing the evolution of macroscopic variables. I then show how the large deviation function of the stationary state of the microscopic system can be used as a Lyapunov function for the macroscopic evolution equations. —————————————————————————— G...