Modified Feynman ratchet with velocity-dependent fluctuations

The randomness of Brownian motion at thermodynamic equilibrium can be spontaneously broken by velocity-dependence of fluctuations, i.e., by dependence of values or probability distributions of fluctuating properties on Brownian-motional velocity. Such randomness-breaking can spontaneously obtain via interaction between Brownian-motional Doppler effects — which manifest the required velocity-dependence — and system geometrical asymmetry. A nonrandom walk is thereby spontaneously superposed on Brownian motion, resulting in a systematic net drift velocity despite thermodynamic equilibrium. The time evolution of this systematic net drift velocity — and of velocity probability density, force, and power output — is derived for a velocity-dependent modification of Feynman’s ratchet. We show that said spontaneous randomness-breaking, and consequent systematic net drift velocity, imply: bias from the Maxwellian of the system’s velocity probability density, the force that tends to accelerate it, and its power output. Maximization, especially of power output, is discussed. Uncompensated decreases in total entropy, challenging the second law of thermodynamics, are thereby implied. PACS numbers: 05.40.Jc, 05.40.Fb, 02.50.Ga, 05.20.Dd, 02.50.Ey, 02.50.Cw. AMS numbers: 60J10, 28D20, 60G50, 82B41, 82B40, 82B05.