A Cost / Speed / Reliability Trade-off to Erasing

TL;DR

This paper models the fundamental tradeoff between speed, reliability, and cost in bit erasure using KL-control, revealing that faster erasing of reliable bits incurs higher costs, with explicit bounds derived.

Contribution

It introduces a novel KL-control framework to quantify the tradeoff between erasing speed, reliability, and cost, providing explicit bounds and insights.

Findings

Rapid erasing of reliable bits costs at least log 2 minus a correction term.

Cost approaches half the log ratio of reliability timescale to erasing timescale when reliability is high.

The framework captures fundamental limits of energy and time in information erasure.

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 $\log 2 - \log\left(1 - \operatorname{e}^{-\frac{\tau_e}{\tau_r}}\right) > \log 2$, which goes to $\frac{1}{2} \log\frac{2\tau_r}{\tau_e}$ when $\tau_r>>\tau_e$.