Demon's variational principle for informational active matter

Abstract: The interplay between information, dissipation, and control is reshaping our understanding of thermodynamics in feedback-regulated systems. We develop the informational Onsager-Machlup principle, a generalized variational framework that unifies energetic, dissipative, and informational contributions within a single formalism. This framework introduces a conditioned Onsager-Machlup integral to quantify path entropy under specified memory states and enables the derivation of cumulant generating functions for arbitrary observables in systems with measurement and feedback. Applying this principle to a minimal model of an information-driven swimmer, where feedback adaptively modulates viscous drag based on velocity measurements, we obtain analytical expressions for the mean velocity and higher-order cumulants. Here, we show that information-based feedback can sustain persistent motion even in dissipative environments, establishing a theoretical foundation for informational active matter and providing a systematic route for designing feedback-powered engines operating far from equilibrium.