From bulk to interface dynamics, in and out of equilibrium

TL;DR

This paper develops a unified framework to analyze interface dynamics in both equilibrium and non-equilibrium systems, deriving relaxation and fluctuation properties using a dynamical-action approach.

Contribution

It introduces a method that applies to a broad class of models, extending existing equilibrium results to non-equilibrium and active field theories.

Findings

Derived linear relaxation of interfaces in various models.

Extended analysis to non-equilibrium and active systems.

Highlighted limitations of common interface ansatz in active theories.

Abstract

We study the dynamics of weakly deformed interfaces separating two stable phases, starting from the fluctuating hydrodynamics of the phase-separating fields. Using a well-chosen definition for the interface and the dynamical-action formalism to represent path probabilities, we derive the linear relaxation of the interface and the fluctuations around it for a large class of models. Our method applies to equilibrium dynamics, where it recovers and complements existing results, but also extends to their non-equilibrium counterparts. We explain how non-linear terms can be systematically computed and illustrate their derivations in the case of (active) model A. We highlight the danger of a popular ansatz used to derive interface dynamics, which was rigorously established in equilibrium but is uncontrolled for active field theories.