Entropy production of a Brownian ellipsoid in the overdamped limit

Abstract

We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here, we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.

Functionals in stochastic thermodynamics: how to interpret stochastic integrals

“…It has been shown [18] that, in presence of temperature gradients, the homogenized Fokker-Planck equation for entropy production acquires non-trivial terms which describe a socalled "entropic anomaly" of the small-mass limit, see also [20,22,23,[32][33][34][35][39][40][41]. In the following, we briefly summarize the calculation and main results from [18], treating explicitly the case in which the friction tensor is not simply proportional to the identity, see also [22]. In stochastic thermodynamics the entropy production (in the thermal environment) is usually defined [2,8,9] as a measure of irreversibility via the log-ratio of probabilities for observing a specific trajectory (x, v) = {(x t , v t )} t f t=0 in forward time versus observing the same trajectory traced out backwards when advancing time.…”

“…and assume that this expression is the asymptotic limit of a (unknown) "generalized entropy production" for vanishing noise correlation time τ b /τ x → 0. For analyzing the small-mass limit τ v /τ x → 0, it proves convenient to split off a boundary term, because we then can rewrite the dv t integral in (34) as a sum of dt and dx t integrals [18,22]. To do so, we first introduce the Maxwell-Boltzmann velocity distribution at given position x and time t,…”

Lorentz forces induce inhomogeneity and flux in active systems

“…Due to the nonconservative nature of the Lorentz force, the overdamped equation of motion cannot be obtained by simply setting the mass of the particles to zero [4,42]. Though there exists a nontrivial limiting procedure [43][44][45] that yields the small-mass limit of the (velocity) Langevin equation, the resulting overdamped equation is not suitable for determining velocity dependent variables such as flux and entropy [4,5,[46][47][48] despite the fact that it captures the position statistics accurately. In this work, we have avoided these problems by performing simulations using the (velocity) Langevin equation with a finite but small mass.…”

Directional transport of propelled Brownian particles confined in a smooth corrugated channel with colored noise

“…Hänggi et al proposed a simple scheme for absolute negative mobility of asymmetry particle in a compartmentalized channel or a rough channel [22]. Marino et al showed the rotational Brownian motion of colloidal particles in the over damped limit generates an additional contribution to the anomalous entropy [23]. Pu et al investigated the reentrant phase separation behavior of active particles with anisotropic Janus interaction, and found that phase separation shows a re-entrance behavior with variation of the Janus interaction strength [24].…”