Calorimetric measurement of work in a quantum system

We propose a calorimetric measurement of work in a quantum system. As a physical realization, we consider a superconducting two-level system, a Cooper-pair box, driven by a gate voltage past an avoided level crossing at charge degeneracy. We demonstrate that, with realistic experimental parameters, the temperature measurement of a resistor (environment) can detect single microwave photons emitted or absorbed by the two-level system. This method would thus be a way to measure the full distribution of work in repeated measurements, and to assess the quantum fluctuation relations.