A Cost/Speed/Reliability tradeoff to erasing

Abstract

We present a Kullback–Leibler (KL) control treatment of the fundamental problem of erasing a bit. We introduce notions of reliability of information storage via a reliability timescale τr , and speed of erasing via an erasing timescale τe . Our problem formulation captures the tradeoff between speed, reliability, and the KL cost required to erase a bit. We show that rapid erasing of a ( ) reliable bit costs at least log 2 − log 1 − e− τr τe > log 2, which goes to 12 log 2τr τe when τr >> τe .