Control protocols for harmonically confined run-and-tumble particles

TL;DR

This paper develops control protocols for a harmonic trap confining run-and-tumble particles, aiming to steer the system between states efficiently and with minimal work, providing insights into optimal active matter control strategies.

Contribution

It introduces a novel differential equation framework for controlling active particles and derives optimal protocols minimizing work in slow transformation regimes.

Findings

Proposed a hierarchy of differential equations for system dynamics.

Derived analytical solutions for minimal work protocols.

Validated protocols through numerical simulations.

Abstract

Run-and-tumble particles constitute one of the simplest models of self-propelled active matter, and provide an ideal playground to the understanding of out-of-equilibrium systems. We consider an idealized setup where one such particle is subject to a harmonic confining potential, and an external agent can vary in time the tumbling rate and the strength of the trap. We search for time-dependent control protocols steering the system between assigned end states, in a prescribed time interval. To this aim, we propose a description of the dynamics, alternative to the usual ones, in the form of an infinite set of ordinary differential equations. Solutions based on a suitable closure of such hierarchy, which we expect to hold true in the limit of long protocol duration, are discussed and compared with numerical simulations. We also look for the protocol completing the task with the minimal work, on average: the problem can be tackled analytically, again in the regime of slow (but not quasi-static) transformations. The solution provides insightful intuition on the optimal strategies for the control of active matter systems.