Quantum Thermodynamics with Degenerate Eigenstate Coherences

We establish quantum thermodynamics for open quantum systems weakly coupled to
their reservoirs when the system exhibits degeneracies. The first and second law of thermodynamics
are derived, as well as a finite-time fluctuation theorem for mechanical work and energy and matter
currents. Using a double quantum dot junction model, local eigenbasis coherences are shown to play
a crucial role on thermodynamics and on the electron counting statistics.