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

reference groups: 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
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].

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