From Brownian motor to Brownian refrigerator

Cooling techniques have a significant impact not only on our everyday life but also on the advances in science. We have come a long way from the primitive method of evaporative cooling, which our body conveniently uses when we perspire, over the evaporation by expansion of a cooling liquid in domestic refrigerators, to high-tech methods including laser cooling, magnetic cooling, radiative cooling or quantum cooling. Temperature is a measure of thermal fluctuations but the latter are not directly observable in macroscopic systems. Recent advances in nanotechnology and molecular biology however allow to manipulate and even manufacture constructions on a molecular scale, where thermal fluctuations can no longer be ignored. To run such machines, we could copy the mode of operation from their macroscopic counterparts. An alternative, and arguably more promising approach, would be to utilize thermal fluctuations rather than fighting them. A well documented example is the Brownian motor [1, 2], which generates power through the rectification of thermal fluctuations. In this letter, we present a novel method of microscopic cooling based on a Brownian motor in which, almost paradoxically, thermal fluctuations themselves can be harnessed to reduce the thermal jitter in one part of the system. Our Brownian motor [3] (see Fig. 1) consists of two parts, a triangle and a flat paddle, which are rigidly linked and move as a single entity along horizontal tracks. Its motion is induced, following Newton’s laws, by the random collisions with the particles of the gas in which it is embedded. Due to the random nature of these collisions, one expects a resulting rather erratic motion of the motor. The question of interest is whether, due to the asymmetry of the triangle, this random motion is characterized by a nonzero average speed in a given direction. When both motor units reside in a single compartment with a gas (or liquid) at equilibrium, we argue that such a sustained motion is impossible because it would violate the second law of thermodynamics. The construction would be a perpetuum mobile of the second kind (or Maxwell demon), because the motion could be used, for example, to lift a weight, hence extract work out of the single heat bath. This impossibility can more deeply be understood from the fact that a system at equilibrium has a perfect time-reversal symmetry. Any movie of such a system, or of any subpart of the system (like monitoring the motion of our motor) is statistically indistinguishable when played forward or backward in time. Hence any form of systematic translation is impossible.