Brownian Refrigerator

Onsager symmetry implies that a Brownian motor, driven by a temperature gradient, will also perform a refrigerator function upon loading. We analytically calculate the corresponding heat flow for an exactly solvable microscopic model and compare it with molecular dynamics simulations.

Figure 1

An asymmetric object on horizontal tracks. (a) Performs Brownian motion with no average systematic drift when in thermal equilibrium. (b) Sustained average systematic motion when subject to a thermal gradient.

Figure 2

The motor of mass $M=2m$ is driven by a constant force satisfying Eq. (10), namely, $F=-0.007$. The temperature of two reservoirs, $T_1$ (dashed line) and $T_2$ (solid line), are initially equal to 1. Clearly the temperature of reservoir 2 ($T_2$) is decreasing, while reservoir 1 is heating up. Note that the average temperature $T_{\mathrm{av}}=(T_1+T_2)/2$ increases due to the Joule heat dissipated in both reservoirs.

Figure 3

The rate of energy change in reservoir 2 as a function of the mass of the motor upon application of a force $F=-0.007$. The energy change encompasses both the heat transfer from reservoir 2 into reservoir 1 as well as the Joule heating in reservoir 2. Cooling is clearly observed.

Figure 4

A rotational version of the proposed refrigerator. (a) A chiral rotor is placed across an insulating wall. (b) A chiral biological molecule will channel heat across a membrane when a small external torque is applied.