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Entropy 2016, 18(5), 165; doi:10.3390/e18050165

A Cost/Speed/Reliability Tradeoff to Erasing

School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai 400005, India
This paper is an extended version of our paper published in the 14th International Conference on Unconventional Computation and Natural Computation (UCNC), Auckland, New Zealand, 30 August–3 September 2015
Academic Editors: John Baez, John Harte, Marc Harper and Adom Giffin
Received: 21 December 2015 / Revised: 21 March 2016 / Accepted: 22 April 2016 / Published: 28 April 2016
(This article belongs to the Special Issue Information and Entropy in Biological Systems)
View Full-Text   |   Download PDF [294 KB, uploaded 28 April 2016]   |  

Abstract

We present a Kullback–Leibler (KL) control treatment of the fundamental problem of erasing a bit. We introduce notions of reliability of information storage via a reliability timescale τ r , and speed of erasing via an erasing timescale τ e . Our problem formulation captures the tradeoff between speed, reliability, and the KL cost required to erase a bit. We show that rapid erasing of a reliable bit costs at least log 2 - log 1 - e - τ e τ r > log 2 , which goes to 1 2 log 2 τ r τ e when τ r > > τ e . View Full-Text
Keywords: erasing; information; thermodynamics; Kullback–Leibler; optimal control; reliability; speed; tradeoff erasing; information; thermodynamics; Kullback–Leibler; optimal control; reliability; speed; tradeoff
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Gopalkrishnan, M. A Cost/Speed/Reliability Tradeoff to Erasing. Entropy 2016, 18, 165.

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