Optimal finite-time bit erasure under full control

TL;DR

This paper derives optimal protocols for finite-time one-bit memory erasure in a controllable double-well potential, minimizing work and exploring trade-offs between erasure completeness, time, and energy costs.

Contribution

It provides explicit formulas and bounds for the minimal work required for finite-time erasure under full control of the potential landscape.

Findings

Minimum work inversely proportional to erasure duration.

Allowing non-equilibrium final states reduces erasure cost.

Explicit bounds on erasure work for various constraints.

Abstract

We study the finite-time erasure of a one-bit memory consisting of a one-dimensional double-well potential, with each well encoding a memory macrostate. We focus on setups that provide full control over the form of the potential-energy landscape and derive protocols that minimize the average work needed to erase the bit over a fixed amount of time. We allow for cases where only some of the information encoded in the bit is erased. For systems required to end up in a local equilibrium state, we calculate the minimum amount of work needed to erase a bit explicitly, in terms of the equilibrium Boltzmann distribution corresponding to the system's initial potential. The minimum work is inversely proportional to the duration of the protocol. The erasure cost may be further reduced by relaxing the requirement for a local-equilibrium final state and allowing for any final distribution compatible with constraints on the probability to be in each memory macrostate. We also derive upper and lower bounds on the erasure cost.