Understanding mechanisms for rectifying stochastic fluctuations has been a long-standing problem in nonequilibrium statistical mechanics. Here, we explore an opportunity provided by nonequilibrium parityviolating metamaterials to uncover new mechanisms for rectification of energy and motion. Using a parityviolating gyroscopic metamaterial that is allowed to interact with a bath of active particles as a model system, we develop an analytic diagrammatic theory that compactly elucidates how the rectification results from an interplay between gyroscopic forces, nonequilibrium activity, and network structure. Our active metamaterial model can generate energy flows through an object in the absence of any temperature gradient. The nonreciprocal microscopic fluctuations responsible for generating the energy flows can further be used to power locomotion in, or exert forces on, a viscous fluid. Taken together, our analytical and numerical results elucidate how the geometry and interparticle interactions of the parity-violating material can couple with the nonequilibrium fluctuations of an active bath and enable rectification of energy and motion.
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