Optimal work associated with off-centered harmonic Brownian motion at any friction damping

Pedro J. Colmenares and Oscar Paredes-Altuve
Phys. Rev. E 104, 034115 – Published 10 September 2021

Abstract

There is extensive literature on how to determine the work involving a Brownian particle interacting with an external field and submerged in a thermal reservoir. However, the information supplied is essentially theoretical without specific calculations to show how this property changes with the system parameters and initial conditions. In this article, we provide explicit calculations of the optimal work considering the particle is under the influence of a time-dependent off-centered moving harmonic potential. It is done for all physical values of the friction coefficient. The system is modeled through a more general version of the Langevin equation which encompasses its classical and quasiclassical version. From the equation that defines the work, the external protocol is found through a fairly current extended version of the Euler-Lagrange equation that unifies the local and nonlocal contributions in a simple expression. The protocol is linear and, unlike previous work, not only changes the initial velocity of the particle but also its acceleration. Calculations were done for friction constants γ spanning all possible values. The periodic γ=1 shows discontinuities in the optimal work of the interplay of concentration and diffusion processes acting periodically in the dynamics. For higher values work appears to be as a smooth function of time, while the truly overdamped, where the inertial effect can be discarded, agrees with the analytical result up to a time where the numerical overdamped algorithm provides a different solution due to its inability to discard entirely the inertial effect.

  • Figure
  • Figure
  • Figure
  • Received 2 June 2021
  • Revised 29 July 2021
  • Accepted 31 August 2021

DOI:https://doi.org/10.1103/PhysRevE.104.034115

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Pedro J. Colmenares*

  • Departamento de Química, Universidad de Los Andes, Mérida 5101, Venezuela

Oscar Paredes-Altuve

  • Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile

  • *Corresponding author: gochocol@gmail.com
  • paredes.oscar@gmail.com

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 104, Iss. 3 — September 2021

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×