Fluctuation Theorem for Partially-masked Nonequilibrium Dynamics

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.