Work as a function of protocol duration for the efficient erasure of an underdamped memory: isothermal to adiabatic transition

Abstract

We use evolutionary reinforcement learning to determine efficient time-dependent erasure protocols for an underdamped cantilever moving in a double-well potential, an experimental realization of a 1-bit memory. We investigate how the mean work $⟨W⟩$ needed to erase a bit scales as a function of the protocol duration $\tau$. We find two regimes, depending on how $\tau$ compares to the relaxation time of the system $t_r$. For $\tau \gg t_r$, the quasistatic isothermal regime, we recover Landauer's bound plus an overhead that scales as $1/\tau$, similar to the overdamped case. By contrast, for $\tau <t_r$ erasure becomes adiabatic and $⟨W⟩$ grows more slowly than in the isothermal case. This growth is bounded from below as $1/\tau$, which we derive using a gedanken optimal protocol. Finally, comparison with overdamped erasure shows that learned protocols can outperform protocols that are optimal subject to equilibrium boundary conditions.