Optimal finite-time thermodynamics of effective two-level systems

The optimization of the conversion of thermal energy into work and the minimization of dissipation for nano- and mesoscopic systems is a complex challenge because of the important role fluctuations play on the dynamics of small systems. I generalize the work of Esposito [] to optimize at all driving speeds the control needed to extract the maximum amount of work from any effective two-level systems. These emerge when one coarse grains degrees of freedom, which is often unavoidable to obtain “real-world” two-level systems. In particular, I allow even for the system to have underlying quantum dynamics, as long as these allow for a coarse graining that leads to a Markovian master equation. I analyze the finite-time thermodynamics of these systems and find the thermodynamically optimal protocols, which depend on the size of the coarse graining needed to obtain a two-level system. Furthermore, I use these results to derive speed limits for any transformation performed on an effective two-level system.