Optimal work associated with off-centered harmonic Brownian motion at any friction damping,Physical Review E

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Optimal work associated with off-centered harmonic Brownian motion at any friction damping
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-10 , DOI: 10.1103/physreve.104.034115
Pedro J Colmenares ₁ , Oscar Paredes-Altuve ₂

Affiliation

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.

中文翻译：

在任何摩擦阻尼下与偏心谐波布朗运动相关的最佳功

关于如何确定布朗粒子与外部场相互作用并淹没在热库中的功，有大量文献。然而，所提供的信息基本上是理论上的，没有具体的计算来显示该属性如何随系统参数和初始条件而变化。在本文中，考虑到粒子受时间相关的偏心移动谐波势的影响，我们提供了最佳工作的明确计算。它适用于摩擦系数的所有物理值。该系统通过朗之万方程的更一般版本进行建模，该方程包含其经典和准经典版本。从定义工作的等式，外部协议是通过 Euler-Lagrange 方程的相当当前的扩展版本找到的，该方程在一个简单的表达式中统一了局部和非局部贡献。该协议是线性的，与以前的工作不同，它不仅改变了粒子的初始速度，还改变了它的加速度。计算了摩擦常数