Autonomous Brownian motor driven by nonadiabatic variation of internal parameters

TL;DR

This paper introduces an autonomous Brownian motor driven by nonadiabatic internal parameter variations, revealing that its average force and velocity depend quadratically on the variation's frequency and amplitude, with no linear response regime.

Contribution

It demonstrates that such a motor operates outside the linear response regime, with quadratic dependence on driving parameters, and shows the limitations of adiabatic and linear approximations.

Findings

Average force and drift velocity are quadratic in frequency and amplitude.

Adiabatic approximation yields zero drift, insufficient to describe the motor.

Linear correction to adiabatic approximation also results in zero drift.

Abstract

We discuss an autonomous motor based on a Brownian particle driven from thermal equilibrium by periodic in time variation of the internal potential through which the particle interacts with molecules of the surrounding thermal bath. We demonstrate for such a motor the absence of a linear response regime: The average driving force and drift velocity are shown to be quadratic in both the frequency and amplitude of the variation. The adiabatic approximation (of an infinitely slow variation) and the leading correction to it (linear in the variation's frequency) both lead to zero drift and are insufficient to describe the motor's operation.