Optimal Finite Time Erasure: A mass transport perspective

Landauer’s principle states that the average heat dissipation in a bit erasure is atleast kBT ln 2. Recent experiments approach this bound in an asymptotic manner with respect to time. Meanwhile, in the experimentally relevant case that a single bit memory is modeled as a Brownian particle in a bistable well, developments in non-equilibrium thermodynamics and stochastic control predict larger heat dissipation for finite time erasure, dependent on the Wasserstein transportation distance between the initial and final configurations. Inspired by these considerations, we propose an experimentally feasible finite time erasure protocol which approximates a Wasserstein geodesic. Monte Carlo simulations are used to demonstrate the efficacy of the proposed erasure protocol, comparing energetics against existing erasure protocols and the theoretically optimal bounds.