Stochastic energetics of a colloidal particle trapped in a viscoelastic bath

TL;DR

This paper derives an analytical framework for understanding energy fluctuations of a colloidal particle in a viscoelastic fluid, validated by experiments, revealing non-mono-exponential decay in position correlations.

Contribution

It provides the first explicit analytical expression for the energy exchange distribution in a non-Markovian viscoelastic environment, linking it to particle position auto-correlations.

Findings

Analytical expression for energy exchange distribution derived.

Experimental validation shows excellent agreement.

Non-mono-exponential decay observed in position auto-correlations.

Abstract

We investigate the statistics of the fluctuations of the energy transfer between an overdamped Brownian particle, whose motion is confined by a stationary harmonic potential, and a surrounding viscoelastic fluid at constant temperature. We derive an analytical expression for the probability density function of the energy exchanged with the fluid over a finite time interval, which implicitly involves the friction memory kernel that encodes the coupling with such a non-Markovian environment, and reduces to the well known expression for the heat distribution in a viscous fluid. We show that, while the odd moments of this distribution are zero, the even moments can be explicitly expressed in terms of the auto-correlation function of the particle position, which generally exhibits a non-mono-exponential decay when the fluid bath is viscoelastic. Our results are verified by experimental measurements for an optically-trapped colloidal bead in semidilute micellar and polymer solutions, finding and excellent agreement for all time intervals over which the energy exchange takes place.