Erratum: Velocity-dependent fluctuations: Breaking the randomness of Brownian motion

Abstract

Any object in thermodynamic equilibrium (TEQ) with a heat bath executes thermal (Brownian) motion. This motion is completely random; i.e., the object is equally likely to move in any direction. This motion is completely random because TEQ is the state of maximum randomness (maximum entropy). In this paper, we prove that if the value of an appropriate fluctuating property of our object functionally depends upon the object's velocity of thermal motion (i.e., if velocity-dependent fluctuations exist), then the randomness of our object's thermal motion at TEQ will be broken---so that, at TEQ, our object will have a net systematic nonrandom drift-velocity component in a preferred direction. This decrease in randomness (in entropy) is shown to occur without any compensating increase either within the object or elsewhere; i.e., it is shown to occur in violation of the second law of thermodynamics. It is also shown how this systematic drift-velocity component can, in turn, be utilized in a process whose only systematic net effect is the conversion, at TEQ, of heat from our heat bath into work, again in violation of the second law of thermodynamics. Both the systematic drift velocity and the time rate of (i.e., the power output associated with) the conversion of heat into work are calculated quantitatively for a simple example.