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Explicit Solution of the Generalised Langevin Equation
Journal of Statistical Physics ( IF 1.6 ) Pub Date : 2020-10-03 , DOI: 10.1007/s10955-020-02639-4
Ivan Di Terlizzi , Felix Ritort , Marco Baiesi

Generating an initial condition for a Langevin equation with memory is a non trivial issue. We introduce a generalisation of the Laplace transform as a useful tool for solving this problem, in which a limit procedure may send the extension of memory effects to arbitrary times in the past. This method allows us to compute average position, work, their variances and the entropy production rate of a particle dragged in a complex fluid by an harmonic potential, which could represent the effect of moving optical tweezers. For initial conditions in equilibrium we generalise the results by van Zon and Cohen, finding the variance of the work for generic protocols of the trap. In addition, we study a particle dragged for a long time captured in an optical trap with constant velocity in a steady state. Our formulas open the door to thermodynamic uncertainty relations in systems with memory.

中文翻译:

广义朗之万方程的显式解

为带记忆的朗之万方程生成初始条件是一个重要的问题。我们引入了拉普拉斯变换的泛化作为解决这个问题的有用工具,其中限制过程可以将记忆效应的扩展发送到过去的任意时间。这种方法允许我们计算平均位置、功、它们的方差和被谐波势拖入复杂流体中的粒子的熵产生率,这可以代表移动光镊的影响。对于平衡中的初始条件,我们概括了 van Zon 和 Cohen 的结果,找到了陷阱通用协议的工作方差。此外,我们研究了在稳定状态下以恒定速度捕获在光阱中的长时间拖动的粒子。
更新日期:2020-10-03
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