Anomalous Heat Dissipation of a Brownian Motor

Abstract

Brownian motors behave completely different than macroscopic Carnot engines because they are kept away from equilibrium by external fluctuations or temperature gradients. Although the studies on the Thermodynamics of these motors have been mainly focused on efficiency, high efficiency may be achieved with considerable heat dissipation losses. In this work the heat dissipation from the motor to two thermal baths is numerically obtained. The process of heat transport is related to the effective temperature through the generalization of the fluctuation-dissipation theorem for systems far from equilibrium. The effective temperature, defined as the comparison between induced and spontaneous fluctuations, can be greater than both reservoir temperatures or can be between them. We found that the heat transport in Brownian motors is different from Fourier's Law and is instead proportional to the nth power of the difference between the effective temperature of the motor and the temperature of the respective bath, where the power n depends only on the temperature of the bath. In this way an expression of anomalous heat transport is obtained as a non-equilibrium measure.