Optimal erasure-work scaling for underdamped memories

Determine the dependence on protocol duration of the minimum mean work required by optimal erasure protocols for underdamped one-bit memories.

Background

The paper studies erasure protocols for a one-bit memory implemented by an underdamped cantilever in a tunable bi-quadratic double-well potential. For overdamped systems with equilibrium end states, optimal transport theory establishes a finite-time overhead proportional to the inverse protocol duration, but no generally applicable optimal protocol is known for underdamped oscillators with weak viscous damping.

The authors use neuroevolutionary reinforcement learning to identify efficient, rather than provably optimal, protocols and find distinct isothermal and adiabatic regimes separated by the system relaxation time. Because the learned protocols are not guaranteed to minimize work, the general duration dependence of the minimum work for optimal underdamped erasure remains unresolved.