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

## TL;DR

This paper analyzes the trade-offs in designing reliable, fast-erasing bits, revealing non-monotonic relationships between friction, erasing speed, and reliability, and identifying optimal designs that minimize operational work.

## Contribution

It introduces a framework for optimizing bit designs by balancing erasing speed, reliability, and energetic costs, highlighting the importance of critical damping conditions.

## Key findings

- Optimal designs saturate erasing time bounds.
- Critical damping enhances reliability beyond minimum requirements.
- Non-monotonic relationships guide parameter space exclusion.

## 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.