Entropy Decrease in Isolated Systems with an Internal Wall undergoing Brownian Motion

We consider an isolated gaseous system, divided in two parts by an adiabatic movable frictionless internal wall undergoing Brownian motion. We show how this kind of motion can lead to a substantial decrease of the system entropy. This surprising result does not violate Boltzmann's H-theorem since the molecular chaos assumption underlying H-theorem is not fulfilled by our system.