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

2024/05/13 by Bernardin, Cédric, Chetrite, Raphaël
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2405.08212

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.

Related

• Macroscopic fluctuation theory of interacting Brownian particles
• A perturbative approach to the macroscopic fluctuation theory
• Notes about the Macroscopic Fluctuating Theory
• Macroscopic Fluctuation Theory versus large-deviation-induced GENERIC
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation