Autonomous Physical Computation: A Categorical Closure Criterion for Physical and Neuromorphic Reservoirs

Abstract

Physical reservoirs, neuromorphic devices, and wave-mediated systems often possess memory, feedback, and rich state-dependent dynamics, but these properties do not by themselves establish autonomous computation. Here we develop a closure criterion for autonomous physical computation, motivated by the wave--particle walker. We formulate the walker as a stroboscopic reservoir with state, where the wave field stores an exponentially decaying trace of previous droplet impacts and guides future motion through local slope coupling. This model separates physical writing, storage, reading, feedback, and externally triggered erasure. We then define computation as robust coarse-grained transition preservation: a physical map implements an abstract transition only when a coarse-graining satisfies compositionality, with abstract states realized by separated physical basins and transitions stable under noise. Autonomous physical computation requires a further closure condition: an internal physical readout state must select the next physical operation. This criterion classifies the wave--particle walker as a wave-memory machine with genuine Turing-like primitives, but not as a closed autonomous physical computer, because the erasing phase shift is externally imposed. The framework turns this distinction into a design principle: memory becomes autonomous computation when physical readout basins are coupled back to operation selection.