  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.
