Adiabatic protocol for the generalized Langevin equation

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.