Information bound on navigation speed in smart active matter

Abstract

Intelligent behavior in life-like systems often arises from the ability to gather, process, and act on information. While active matter provides a framework for studying life-like dynamics, it typically omits internal information-processing and decision-making. Here we introduce an adaptive active particle model that uses minimal information processing capabilities in order to navigate towards a distant target. By combining renewal-based intermittent motion with the Cram\'{e}r-Rao inequality, we derive a bound on the navigation speed valid for a wide range of information processing strategies. The framework captures hallmark features of cognitive systems, including optimal sensing durations and a speed-accuracy trade-off that balances noise and reliability. Allowing stored information to degrade before action reveals that although deterioration slows navigation, the trade-off remains governed primarily by external orientational noise and is remarkably insensitive to memory decay.