Fractional Macroscopic Fluctuation Theory for a Superdiffusive Ginzburg-Landau dynamics

Cedric Bernardin; Patricia Gonçalves; João Pedro Mangi

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arXiv · 2603.25957

Fractional Macroscopic Fluctuation Theory for a Superdiffusive Ginzburg-Landau dynamics

Cedric Bernardin·Patricia Gonçalves·João Pedro Mangi

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Abstract

We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the corresponding stationary profile is characterized by a fractional Laplace equation. We establish a dynamical large deviations principle for the empirical measure and derive the associated stationary large deviations principle for the non-equilibrium steady state, which can be computed semi-explicitly. We further show that the stationary rate function coincides with the quasi-potential associated with the dynamical large deviations functional.

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Cedric Bernardin, Patricia Gonçalves, João Pedro Mangi. 2026-03-26. Fractional Macroscopic Fluctuation Theory for a Superdiffusive Ginzburg-Landau dynamics. https://arxiv.org/abs/2603.25957

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