Optimal work of Brownian motion in a harmonic time-dependent stiffness potential. Effect of the initial position (2302.01299v1)

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.