# A Cost / Speed / Reliability Trade-off in Erasing a Bit

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reference groups
Computer Science Theory
General Non-equilibrium Statistical Physics
Stochastic Thermodynamics
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authors
Manoj Gopalkrishnan
title
A Cost / Speed / Reliability Trade-off in Erasing a Bit
type
journal
year
2015
abstract
We present a Kullback-Leibler (KL) control treatment of the fundamental problem of erasing a bit. We introduce notions of ${\displaystyle {\textbf {reliability}}}$ 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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