Gaussian Feedback With Atypical Structure: Steering Flows in Path Space

We formulate a variational theory of continuous-time feedback communication based on controlled posterior stochastic flows. The fundamental action functional is defined as the pathspace relative entropy between controlled and passive posterior-flow laws. Using Girsanov theory, innovations decompositions, and continuous-time directed information identities, we show that the Aryabhata action coincides with causal entropy production and converges asymptotically to the directed-information rate. The resulting framework unifies stochastic filtering, KL-control, large deviations, and feedback information theory.