  We provide a unified thermodynamic formalism describing information transfers
in autonomous as well as nonautonomous systems described by stochastic
thermodynamics. We demonstrate how information is continuously generated in an
auxiliary system and then transferred to a relevant system that can utilize it
to fuel otherwise impossible processes. Indeed, while the joint system
satisfies the second law, the entropy balance for the relevant system is
modified by an information term related to the mutual information rate between
the two systems. We show that many important results previously derived for
nonautonomous Maxwell demons can be recovered from our formalism and use a
cycle decomposition to analyze the continuous information flow in autonomous
systems operating at steady-state. A model system is used to illustrate our
findings.
