Entropic equality for worst-case work at any protocol speed

Understand

We derive an equality for non-equilibrium statistical mechanics in finite-dimensional quantum systems.

• The equality concerns the worst-case work output of a time-dependent Hamiltonian protocol in the presence of a Markovian heat bath.
• It has has the form "worst-case work = penalty - optimum".
• The equality holds for all rates of changing the Hamiltonian and can be used to derive the optimum by setting the penalty to 0.