# 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...") |
(use Math) |
||

Line 9: | Line 9: | ||

|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 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 .

## Counts

- Citation count
- Page views
- 14

## Identifiers

**doi:**https://doi.org/10.3390/e18050165 (Google search)**arxiv:**1410.1710**websites:**http://arxiv.org/abs/1410.1710