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

Latest revision as of 15:19, April 29, 2019

reference groups: Computer Science Theory; General Non-equilibrium Statistical Physics; Stochastic Thermodynamics
author-supplied keywords
keywords
authors: Manoj Gopalkrishnan
title: A cost/speed/reliability tradeoff to erasing
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 [math]\displaystyle{ \tau_r }[/math], and "speed" of erasing via an erasing timescale [math]\displaystyle{ \tau_e }[/math]. 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 [math]\displaystyle{ \log 2 - \log\left(1 - \operatorname{e}^{-\frac{\tau_e}{\tau_r}}\right) \gt \log 2 }[/math], which goes to [math]\displaystyle{ \frac{1}{2} \log\frac{2\tau_r}{\tau_e} }[/math] when [math]\displaystyle{ \tau_r\gt \gt \tau_e }[/math].

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 |scopus=2-s2.0-84943625259
 |pui=606383559
-|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 <math>\log 2 - \log\left(1 - \operatorname{e}^{-\frac{\tau_e}{\tau_r}}\right) > \log 2</math>, which goes to <math>\frac{1}{2} \log\frac{2\tau_r}{\tau_e}</math> when <math>\tau_r>>\tau_e</math>.
+|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 <math>\tau_r</math>, and "speed" of erasing via an erasing timescale <math>\tau_e</math>. 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 <math>\log 2 - \log\left(1 - \operatorname{e}^{-\frac{\tau_e}{\tau_r}}\right) > \log 2</math>, which goes to <math>\frac{1}{2} \log\frac{2\tau_r}{\tau_e}</math> when <math>\tau_r>>\tau_e</math>.
 |Mendeley link=http://www.mendeley.com/research/costspeedreliability-tradeoff-erasing
 |pages=192-201