  We establish a novel generalization of the fluctuation theorem for
partially-masked nonequilibrium dynamics. We introduce a partial entropy
production with a subset of all possible transitions, and show that the partial
entropy production satisfies the integral fluctuation theorem.Our result
reveals the fundamental properties of a broad class of autonomous nanomachines
as well as non-autonomous ones. In particular, our result gives a unified
fluctuation theorem for both autonomous and non-autonomous Maxwell's demons,
where mutual information plays a crucial role. Furthermore, we derive a novel
kind of fluctuation-dissipation theorem that relates nonequilibrium stationary
current to two kinds of equilibrium fluctuations.
