Autonomous Physical Computation: A Categorical Closure Criterion for Physical and Neuromorphic Reservoirs
2026-07-27 • Emerging Technologies
Emerging Technologies
AI summaryⓘ
The authors explore what makes a physical system able to perform its own computations without outside help. Using a model based on a walking droplet influenced by waves it created earlier, they break down how memory, reading, and feedback work in such systems. They argue that for a system to be truly autonomous in computing, it must internally decide what to do next without external inputs. Their analysis shows the walking droplet system has key computation abilities but still relies on outside signals to erase memory, so it isn't fully independent. This work helps clarify when and how physical systems can self-compute by connecting memory and control internally.
physical reservoirneuromorphic deviceswave-particle walkerstroboscopic reservoirmemoryfeedbackcoarse-grainingTuring machineautonomous computationphase shift
Authors
Nima Dehghani
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.