Speaker
Description
In this paper we address and propose a solution to the problem of the definition of work in quantum mechanics. We define a work operator for driven quantum systems by recasting the problem in an automatized picture, where the driving of the system is replaced by a time-independent interaction with a battery. In this energy-conserving setting, the work operator is recovered as the energy that left the battery, thereby providing an operational definition of work that describes both classical and quantum statistics. Within this framework, the exchanged energy is not determined solely by the energy eigenvalues accessed by the two-point measurement scheme, but can also depend on off-diagonal coherences, which must therefore be included for a complete energetic description. We present an explicit protocol in which such coherence contributions are essential and a work operator is required to account fully for the energetics. We then derive a general quantum fluctuation theorem for this work operator, which recovers the Jarzynski equality as a special case in the appropriate classical regime. This also clarifies why our construction remains compatible with the previous no-go theorem for work fluctuations, since the relevant classical limit is more restrictive than mere diagonality in the initial energy basis. Our results thereby provide a framework for describing work and energy exchange in coherent quantum processes beyond the two-point measurement scheme, and open fascinating avenues for investigating the emergence of a quantum arrow of time.