Macroscopic Fluctuation Theory for Ginzburg-Landau dynamics with long range interactions

TL;DR

This paper extends the Macroscopic Fluctuation Theory to Ginzburg-Landau dynamics with long-range interactions, resulting in non-linear fractional diffusion equations that describe macroscopic behavior.

Contribution

It introduces a novel extension of MFT to systems with long-range interactions, leading to non-linear fractional diffusion equations.

Findings

Derivation of macroscopic equations as non-linear fractional diffusion equations.

Extension of MFT framework to long-range interacting systems.

Potential applications in understanding complex diffusive phenomena.

Abstract

Focusing on a famous class of interacting diffusion processes called Ginzburg-Landau (GL) dynamics, we extend the Macroscopic Fluctuations Theory (MFT) to these systems in the case where the interactions are long-range, and consequently, the macroscopic effective equations are described by non-linear fractional diffusion equations.