Thermodynamic cost of erasing information in finite time

The Landauer principle sets a fundamental thermodynamic constraint on the minimum amount of heat that must be dissipated to erase one logical bit information through quasistatically slow protocol. For finite time erasure, costs depend specific physical realization memory and how is erased. Here we treat problem within paradigm Brownian particle in symmetric double-well potential. two minima represent values bit, 0 1, particle's position current state memory. erasure protocol realized by applying an external time-dependent tilting force. We derive analytical tools evaluate work required classical via arbitrary continuous protocol, which relevant setting for practical applications. Importantly, our method not restricted average work, but instead gives access full distribution arising from many independent realizations process. Using common example changes linearly with acting double-parabolic potential, explicitly calculate all quantities verify them numerically.