Fluctuations and response in a non-equilibrium micron-sized system

TL;DR

This paper presents a generalized fluctuation-dissipation relation for non-equilibrium systems with Markovian dynamics, validated through experiments on a driven Brownian particle in a toroidal optical trap, applicable to various micron-sized systems.

Contribution

It introduces a new fluctuation-dissipation relation involving entropy and dynamical activity correlations, validated experimentally in a non-equilibrium Brownian system.

Findings

Experimental verification of the generalized fluctuation-dissipation relation.

Successful measurement of linear response in a non-equilibrium optical trap system.

Applicability of the approach to diverse micron-sized non-equilibrium systems.

Abstract

The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two correlation functions of the observable of interest: one with the entropy excess and the second with the excess of dynamical activity with respect to the unperturbed process, without recourse to anything but the dynamics of the system. We illustrate this approach in the experimental determination of the linear response of the potential energy of a Brownian particle in a toroidal optical trap. The overdamped particle motion is effectively confined to a circle, undergoing a periodic potential and driven out of equilibrium by a non-conservative force. Independent direct and indirect measurements of the linear response around a non-equilibrium steady state are performed in this simple experimental system. The same ideas are applicable to the measurement of the response of more general non-equilibrium micron-sized systems immersed in Newtonian fluids either in stationary or non-stationary states and possibly including inertial degrees of freedom.