Optimal work of Brownian motion in a harmonic time-dependent stiffness potential. Effect of the initial position

TL;DR

This paper investigates the optimal work done on a Brownian particle in a harmonic potential with time-dependent stiffness, considering specific initial positions and analyzing entropy and information aspects, extending previous overdamped results.

Contribution

It extends prior work by solving the Langevin equation for specific initial conditions and analyzing the role of initial position, entropy, and information in the work optimization.

Findings

Optimal work depends on initial position.

Maxwell's demon effect observed under certain conditions.

Results align with numerical simulations.

Abstract

The system consists of a Brownian particle immersed in a heat bath trapped in optical tweezers with a time-dependent strength acting as an external protocol. In [Phys. Rev. Letts., 98:108301, 2007] the optimal mean work in the overdamped regime was thoroughly calculated by assuming the work must be averaged over the distribution of the initial position of the particle. The present research assumes instead the solution of the Langevin equation for any given initial position and its average done over the noise distribution. Therefore, this proposal extends in a more general sense the results already published, including the appearance of Maxwell's demon for particular initial conditions which is analyzed in terms of entropy production rate and the mutual information obtained by measuring the particle position. The proposed research has the advantage of being able to be compared with data from numerical simulations.