A central topic in the emerging field of quantum thermodynamics is the
definition of thermodynamic work in the quantum regime. One widely used
solution is to define work for a closed system undergoing non-equilibrium
dynamics according to the two-point energy measurement scheme. However, due to
the invasive nature of measurement the two-point quantum work probability
distribution leads to inconsistencies with two pillars of thermodynamics: it
breaks the first law and the time-reversal symmetry expected for closed
dynamics. We here introduce the quantum histories framework as a method to
characterise the thermodynamic properties of the unmeasured, closed dynamics.
Extending the classical phase space trajectories to continuous power operator
trajectories allows us to derive an alternative quantum work distribution for
closed quantum dynamics that fulfils the first law and is time-reversal
symmetric. We find that the work distribution of the unmeasured dynamics leads
to deviations from the classical Jarzynski equality and can have negative
values highlighting distinctly non-classical features of quantum work.Comment: 18 pages, 2 figures, comments welcom
