  We derive a general fluctuation theorem for quantum maps. The theorem applies
to a broad class of quantum dynamics, such as unitary evolution, decoherence,
thermalization, and other types of evolution for quantum open systems. The
theorem reproduces well-known fluctuation theorems in a single and simplified
framework and extends the Hatano-Sasa theorem to quantum nonequilibrium
processes. Moreover, it helps to elucidate the physical nature of the
environment inducing a given dynamics in an open quantum system.
