Adiabatic protocol for the generalized Langevin equation

TL;DR

This paper introduces a self-consistent adiabatic protocol for Brownian particles in optical traps based on a generalized Langevin equation, avoiding external optimization by leveraging intrinsic system parameters.

Contribution

It presents a novel methodology for determining adiabatic work that depends solely on system properties and involves an integral equation for protocol optimization.

Findings

The protocol depends on the system's dynamical properties without external optimization.

It is characterized by intrinsic parameters only.

An integral equation is derived for protocol optimization along the trajectory.

Abstract

This article proposes a self-consistent methodology for determining the mechanical adiabatic work of Brownian particles trapped in optical tweezers. Rather than varying the trap frequency, the proposed protocol involves displacing the trap according to a predefined schedule. Assuming the dynamics obey a modified generalized Langevin equation previously introduced by the author, we find that the external driving depends on the system's dynamical properties and, in contrast to isothermal processes, does not require external optimization. The model is fully characterized by its intrinsic parameters, requiring no additional variables. Furthermore, it is shown that along the particle trajectory, the protocol must be optimized and expressed as an integral equation.