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A central topic in the emerging field of quantum thermodynamics is thedefinition of thermodynamic work in the quantum regime. One widely usedsolution is to define work for a closed system undergoing non-equilibriumdynamics according to the two-point energy measurement scheme. However, due tothe invasive nature of measurement the two-point quantum work probabilitydistribution leads to inconsistencies with two pillars of thermodynamics: itbreaks the first law and the time-reversal symmetry expected for closeddynamics. We here introduce the quantum histories framework as a method tocharacterise the thermodynamic properties of the unmeasured, closed dynamics.Extending the classical phase space trajectories to continuous power operatortrajectories allows us to derive an alternative quantum work distribution forclosed quantum dynamics that fulfils the first law and is time-reversalsymmetric. We find that the work distribution of the unmeasured dynamics leadsto deviations from the classical Jarzynski equality and can have negativevalues highlighting distinctly non-classical features of quantum work.

Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework