Stochastic energetics of a colloidal particle trapped in a viscoelastic bath

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 autocorrelation 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.

An active fractional Ornstein–Uhlenbeck particle: diffusion and dissipation

“…The overdamped limit of the AOUP is considered in [37], whereas the dynamics of colloidal particles in a harmonic trap are described by an active Smoluchowski equation. Recently, an investigation of the energetics of a particle in the presence of a viscoelastic medium has been reported [41]. It is worth mentioning that most of the related works on the AOUP preserve the Markovianity of the medium.…”

“…There are some memory kernels that satisfy this limiting case, such as an exponential memory kernel, which is usually utilized to describe the memory effect or rheological response of viscoelastic materials, such as intracellular fluid and polymer solutions [41,53], that can induce additional dissipative effects on the system [54,55]. However, the particular choice of considering a power-law memory kernel stems from the idea that it still encompasses the additional dissipative effect of the exponential kernel while inducing long-range dependency.…”

“…We now consider the presented model in the presence of a harmonic potential; such a potential can be realized using optical tweezers [26,41,64,65] to generate an optical trap with stiffness k that is capable of localizing the probed particle. Assuming that the particle is in equilibrium with the medium (without the active noise), we then allow the presence of active noise to drive it away from equilibrium at t = 0.…”