Linear response of hydrodynamically-coupled particles under a nonequilibrium reservoir

TL;DR

This paper develops a linear response theory for nonequilibrium overdamped systems with hydrodynamic interactions, using experimental-like simulations to connect theoretical predictions with measurable correlations.

Contribution

It introduces a novel response framework for nonequilibrium systems with hydrodynamic coupling, including the effects of a non-equilibrium reservoir, and links response functions to correlation functions.

Findings

Response to mechanical forcing derived from correlation functions.

Response to temperature variations expressed through path-weight action.

Simulation results support the theoretical predictions.

Abstract

A recent experiment driving colloids electromagnetically, by B\'erut et al. [2014 Europhys. Lett. 107, 60004], is an ideal paradigm for illustrating a linear response theory for nonequilibrium overdamped systems including hydrodynamic interactions and, unusually, a reservoir itself out of equilibrium. Indeed, in this setup one finds a nonequilibrium environment in which the mobility and diffusivity of free particles are not simply proportional to each other. We derive both the response to a mechanical forcing and to temperature variations in terms of correlations between an observable and a path-weight action. The time-antisymmetric component of the latter turns out not to be simply proportional to the heat flowing into the environment. These results are visualized with simulations resembling conditions and protocols easily realizable in the experiment, thereby tracing a path for experimental verifications of the theory.