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

TL;DR

This paper investigates the large-deviation functional in boundary-driven diffusive systems, revealing non-differentiable singularities unique to non-equilibrium conditions through exact solutions and simulations.

Contribution

It demonstrates the existence of singularities in the large-deviation functional of non-equilibrium diffusive systems, linking them to broken time-reversal symmetry and boundary conditions.

Findings

Singularities in large-deviation functionals are demonstrated in an exactly-solvable model.

Numerical simulations confirm the presence of singularities in boundary-driven Ising models.

Singular behavior is linked to minima in the system's compressibility.

Abstract

We study the probability of arbitrary density profiles in conserving diffusive fields which are driven by the boundaries. We demonstrate the existence of singularities in the large-deviation functional, the direct analog of the free-energy in non-equilibrium systems. These singularities are unique to non-equilibrium systems and are a direct consequence of the breaking of time-reversal symmetry. This is demonstrated in an exactly-solvable model and also in numerical simulations on a boundary-driven Ising model. We argue that this singular behavior is expected to occur in models where the compressibility has a deep enough minimum. The mechanism is explained using a simple model.