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Non-equilibrium quantum fluctuations of work

The concept of work is basic for statistical thermodynamics. To gain a fuller understanding of work and its (quantum) features, it needs to be represented as an average of a fluctuating quantity. Here I focus on the work done between two moments of time for a thermally isolated quantum system driven by a time-dependent Hamiltonian. I formulate two natural conditions needed for the fluctuating work to be physically meaningful for a system that starts its evolution from a non-equilibrium state. The existing definitions do not satisfy these conditions due to issues that are traced back to non-commutativity. I propose a definition of fluctuating work that is free of previous drawbacks and that applies for a wide class of non-equilibrium initial states. It allows to deduce a generalized (out of equilibrium) work-fluctuation theorem.