  Assigning the variations of internal energy into heat or work contributions
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, in addition to the
conventional approach, two definitions motivated by either classical work or
heat, in which the driving Hamiltonian or 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. Our results illustrate the
trajectory-dependent character of heat and work, and how contributions
originally assigned to dissipation in the Lindblad equation can become coherent
part assigned to work.
