Thermodynamics with Continuous Information Flow

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