Colmenares Pedro J, Paredes-Altuve Oscar
Departamento de Química, Universidad de Los Andes, Mérida 5101, Venezuela.
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile.
Phys Rev E. 2021 Sep;104(3-1):034115. doi: 10.1103/PhysRevE.104.034115.
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.
关于如何确定涉及与外部场相互作用并浸没在热库中的布朗粒子的功，已有大量文献。然而，所提供的信息本质上是理论性的，没有具体计算来表明该性质如何随系统参数和初始条件变化。在本文中，我们考虑粒子受到随时间变化的偏心移动谐振势的影响，提供了最优功的显式计算。这是针对摩擦系数的所有物理值进行的。该系统通过朗之万方程的一个更通用版本进行建模，该版本涵盖了其经典和准经典版本。从定义功的方程出发，通过一个相当新的扩展版本的欧拉 - 拉格朗日方程找到外部协议，该方程在一个简单表达式中统一了局部和非局部贡献。该协议是线性的，与之前的工作不同，它不仅改变粒子的初始速度，还改变其加速度。针对跨越所有可能值的摩擦常数γ进行了计算。周期性的γ = 1在动力学中周期性作用的浓度和扩散过程相互作用的最优功中显示出不连续性。对于更高的值，功似乎是时间的平滑函数，而在真正的过阻尼情况下，惯性效应可以忽略不计，在数值过阻尼算法由于无法完全忽略惯性效应而提供不同解之前的一段时间内，它与解析结果一致。
