  Operational quantum stochastic thermodynamics is a recently proposed theory
to study the thermodynamics of open systems based on the rigorous notion of a
quantum stochastic process or quantum causal model. In there, a stochastic
trajectory is defined solely in terms of experimentally accessible measurement
results, which serve as the basis to define the corresponding thermodynamic
quantities. In contrast to this observer-dependent point of view, a `black
box', which evolves unitarily and can simulate a quantum causal model, is
constructed here. The quantum thermodynamics of this big isolated system can
then be studied using widely accepted arguments from statistical mechanics. It
is shown that the resulting definitions of internal energy, heat, work, and
entropy have a natural extension to the trajectory level. The canonical choice
of them coincides with the proclaimed definitions of operational quantum
stochastic thermodynamics, thereby providing strong support in favour of that
novel framework. However, a few remaining ambiguities in the definition of
stochastic work and heat are also discovered and in light of these findings
some other proposals are reconsidered. Finally, it is demonstrated that the
first and second law hold for an even wider range of scenarios than previously
thought, covering a large class of quantum causal models based solely on a
single assumption about the initial system-bath state.
