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Thermodynamics of Computation

Difference between revisions of "A Cost / Speed / Reliability Trade-off in Erasing a Bit"

From Thermodynamics of Computation
(Created page with "{{Reference Material |title=A Cost / Speed / Reliability Trade-off in Erasing a Bit |reference groups=Computer Science Theory, General Non-equilibrium Statistical Physics, Sto...")
 
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|doi=https://doi.org/10.3390/e18050165
 
|doi=https://doi.org/10.3390/e18050165
 
|arxiv=1410.1710
 
|arxiv=1410.1710
|abstract=We present a Kullback-Leibler (KL) control treatment of the fundamental problem of erasing a bit. We introduce notions of \textbf{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 $\log 2 - \log\left(1 - \operatorname{e}^{-\frac{\tau_e}{\tau_r}}\right) > \log 2$, which goes to $\frac{1}{2} \log\frac{2\tau_r}{\tau_e}$ when $\tau_r>>\tau_e$.
+
|abstract=We present a Kullback-Leibler (KL) control treatment of the fundamental problem of erasing a bit. We introduce notions of <math>\textbf{reliability}</math> 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/cost-speed-reliability-tradeoff-erasing-bit
 
|Mendeley link=http://www.mendeley.com/research/cost-speed-reliability-tradeoff-erasing-bit
 
|month=April
 
|month=April

Latest revision as of 09:21, 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 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 of information storage via a reliability timescale , and speed of erasing via an erasing timescale . 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 , which goes to when .


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