# Editing A cost/speed/reliability tradeoff to erasing

From Thermodynamics of Computation

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|scopus=2-s2.0-84943625259 | |scopus=2-s2.0-84943625259 | ||

|pui=606383559 | |pui=606383559 | ||

β | |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 | + | |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>. |

|Mendeley link=http://www.mendeley.com/research/costspeedreliability-tradeoff-erasing | |Mendeley link=http://www.mendeley.com/research/costspeedreliability-tradeoff-erasing | ||

|pages=192-201 | |pages=192-201 |