Designing the Optimal Bit: Balancing Energetic Cost, Speed and Reliability

Abstract

We consider the technologically relevant costs of operating a reliable bit that can be erased rapidly. We find that both erasing and reliability times are non-monotonic in the underlying friction, leading to a trade-off between erasing speed and bit reliability. Fast erasure is possible at the expense of low reliability at moderate friction, and high reliability comes at the expense of slow erasure in the underdamped and overdamped limits. Within a given class of bit parameters and control strategies, we define "optimal" designs of bits that meet the desired reliability and erasing time requirements with the lowest operational work cost. We find that optimal designs always saturate the bound on the erasing time requirement, but can exceed the required reliability time if critically damped. The non-trivial geometry of the reliability and erasing time-scales allows us to exclude large regions of parameter space as sub-optimal. We find that optimal designs are either critically damped or close to critical damping under the erasing procedure.

37 pages, 22 figures, Section 4 shortened by moving proofs to the Supplementary Information, Section A.2 added to the Supplementary Information to introduce accuracy of erasure, small clarifications added throughout, To appear in the Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Cited by in corpus (7)

• Finite-time Landauer principle
• Universal Bound on Energy Cost of Bit Reset in Finite Time
• Dynamics of information erasure and extension of Landauer's bound to fast processes
• Optimal Control of Underdamped Systems: An Analytic Approach
• Minimal work protocols for inertial particles in non-harmonic traps
• Simulation of reversible molecular mechanical logic gates and circuits
• A Shortcut to Finite-time Memory Erasure