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

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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

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year

2015

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

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15

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• doi: https://doi.org/10.3390/e18050165 (Google search)
• arxiv: 1410.1710\right) > \log 2$, which goes to $\frac{1}{2} \log\frac{2\tau_r}{\tau_e}$ when $\tau_r>>\tau_e$.

|Mendeley link=http://www.mendeley.com/research/cost-speed-reliability-tradeoff-erasing-bit |month=April |day=28 |date published=28 April 2016 |websites=http://arxiv.org/abs/1410.1710 }}