Thermodynamic Cost of Recurrent Erasure

Abstract

Recent experiments have implemented resetting by means of a time-varying external harmonic trap whereby the trap stiffness is changed from an initial to a final value in finite-time and then the system is reset when it relaxes to an equilibrium distribution in the final trap. Such setups are very similar to those studied in the context of the finite-time Landauer erasure principle. We analyze the thermodynamic costs of such a setup by deriving a moment generating function for the work cost of recurrently changing the trap stiffness in finite-time, thereby maintaining a non-equilibrium steady state. We analyze the mean and variance of the work required for a specific experimentally viable protocol and also obtain an optimal protocol which minimizes the mean cost. For both these procedures, our analysis captures both the large-time and short-time corrections. For the optimal protocol, we obtain a closed form expression for the mean cost for all protocol durations, thereby making contact with earlier work on geometric measures of dissipation-minimizing optimal protocols that implement information erasure.