  Assigning changes of internal energy to heat or work is a challenging task
due to the fact that these properties are trajectory dependent. A number of
proposals have been put forward for open quantum systems following an arbitrary
dynamics. We here focus on non-equilibrium thermodynamics of a two-level system
and explore two approaches, one motivated by definition of classical work, the
other by heat, and in which the driving Hamiltonian and the trajectory itself
are respectively used to set up a reference basis. We first give the
thermodynamic properties for an arbitrary dynamics and illustrate the results
on the Bloch sphere. Then, we solve the particular example of a periodically
driven qubit interacting with a dissipative and decoherence bath. The results
illustrate the difference between the two considered approaches, that can be
maximal in this model.
