Difference between revisions of "A Cost / Speed / Reliability Trade-off in Erasing a Bit"
From Thermodynamics of Computation
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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 | + | |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 15:21, 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 [math]\displaystyle{ \textbf{reliability} }[/math] 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].
Counts
- Citation count
- Page views
- 15
Identifiers
- doi: https://doi.org/10.3390/e18050165 (Google search)
- arxiv: 1410.1710
- websites: http://arxiv.org/abs/1410.1710
