# Difference between revisions of "A cost/speed/reliability tradeoff to erasing"

reference groups
Computer Science Theory
General Non-equilibrium Statistical Physics
Stochastic Thermodynamics
author-supplied keywords
keywords
authors
Manoj Gopalkrishnan
title
type
conference_proceedings
year
2015
pages
192-201
volume
9252
publisher
Springer Verlag
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 ${\displaystyle \tau _{r}}$, and "speed" of erasing via an erasing timescale ${\displaystyle \tau _{e}}$. 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 ${\displaystyle \log 2-\log \left(1-\operatorname {e} ^{-{\frac {\tau _{e}}{\tau _{r}}}}\right)>\log 2}$, which goes to ${\displaystyle {\frac {1}{2}}\log {\frac {2\tau _{r}}{\tau _{e}}}}$ when ${\displaystyle \tau _{r}>>\tau _{e}}$.

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