Thermodynamic work associated to quantum Brownian motion in an external field

TL;DR

This paper investigates the thermodynamic work done on a quantum Brownian particle in an external field, revealing how energy minimization constrains the optimal protocol and depends on the fluid's friction coefficient.

Contribution

It introduces a variational approach to determine the minimal work protocol for a quantum Brownian particle influenced by an external field.

Findings

Energy reaches a minimum under certain protocol restrictions.

The minimal energy depends solely on the friction coefficient.

The work functional is non-local and minimized using a variational principle.

Abstract

This work focuses on the response to an external field of a Brownian particle submerged in an Ohmic quantum thermal bath. The field only affects the dynamics of the central particle without affecting the thermal reservoir. The thermodynamic function to be analyzed is the average work due only to the external force. Being energy a non-local function of the protocol, a standard variational principle is used to derive it. It was found that the energy reaches a minimum imposing a restriction on the optimal protocol. This is found by applying the variational principle to the non-local work functional.It is also a minimum and only depends of the friction coefficient of the surrounding fluid.