Minimal energy dissipation and maximal error for the computational process

Abstract

In a preceding paper, the execution of elementary logic steps was analyzed for minimal energy requirements and for bounds on the unavoidable error probabilities. This was done with the aid of a hypothetical device involving the use of a particle held in a time-modulated potential well, and coupled through springs to other such particles. The previous analysis was limited to the case of wells modulated very slowly compared to the relaxation time for particle redistribution. The present analysis extends these studies to the case of computations proceeding at arbitrary velocity. The same hypothetical device is invoked, with minor modifications for analytical tractability. Energy dissipation is found to be minimal for potential wells endowed with critical damping and the dissipation is roughly proportional to computing rate. The error rate also increases with computing velocity and is lowered by critical damping, but is less sensitive to these parameters, and is largely dependent on the magnitude of the interaction potentials between wells. © 1971 The American Institute of Physics.