Drift and Diffusion in Reversible Computation

Abstract

We provide a brief introduction to questions about the fundamental physical limitations of the computational process, and to reversible computation, without any attempt to repeat more complete and self-contained discussions. We explicitly question, in connection with the existing quantum mechanical descriptions of the computational process, whether the Hamiltonians invoked in these descriptions correspond to the modest number of parts considered to be reasonable for a computer. Our main goal, however, is an analysis of classical reversible computers, in the presence of noise and friction. Such computers can be driven by an externally applied driving force, independent of time and of the computational progress. Alternatively, they can be driven by time dependent force fields, much as ordinary computers are clocked. It is shown that clocked reversible computers can minimize the ratio of diffusion, i.e. unpredictability in the progress of the computation, relative to the intended speed of motion. The analysis emphasizes the case of heavily damped systems, but indicates that lightly damped systems behave similarly.