A Cost / Speed / Reliability Trade-off to Erasing

Abstract

We present a KL-control treatment of the fundamental problem of erasing a bit. We introduce notions of "reliability" of information storage via a reliability timescale ${\tau }_r$, and "speed" of erasing via an erasing timescale ${\tau }_e$. Our problem formulation captures the tradeoff between speed, reliability, and the Kullback-Leibler (KL) cost required to erase a bit. We show that rapid erasing of a reliable bit costs at least $\log 2-\log \left(1-e^{-\frac{{\tau }_e}{{\tau }_r}}\right)>\log 2$, which goes to $\frac{1}{2}\log \frac{2{\tau }_r}{{\tau }_e}$ when ${\tau }_r>>{\tau }_e$.

arXiv comment14 pages, 3 figures. Conference version: Unconventional Computation and Natural Computation (2015), pp. 192--201, Springer International Publishing. Changes: Section 4 is substantially expanded with a discussion of possible physical meanings for the KL-cost function