Finite-time Landauer principle at strong coupling

Landauer's principle gives a fundamental limit to the thermodynamic cost of erasing information. Its saturation requires a reversible isothermal process, and hence infinite time. We develop a finite-time version of Landauer's principle for a quantum dot strongly coupled to a fermionic bath. By solving the exact non-equilibrium dynamics, we optimize erasure processes (taking both the dot's energy and system-bath coupling as control parameters) in the slow driving regime through a geometric approach to thermodynamics. We find analytic expressions for the thermodynamic metric and geodesic equations, which can be solved numerically. Their solution yields optimal finite-time processes that allow us to characterize a fundamental finite-time correction to Landauer's bound, fully taking into account non-markovian and strong coupling effects.