A Cost/Speed/Reliability Tradeoff to Erasing

摘要

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 τ_r, and speed of erasing via an erasing timescale τ_e. Our problem formulation captures the tradeoff between speed, reliability, and the Kullback-Leibler (KL) cost required to erase a bit. We show that erasing a reliable bit fast costs at least log 2 - log (1 - e~(-τ_e/τ_r)) > log 2, which goes to 1/2 log 2_(τ_r)/τ_e when τ_r τ_e.