Information Bound on Navigation Speed in Smart Active Matter

Intelligent behavior in lifelike systems often arises from the ability to gather, process, and act on information. While active matter provides a framework for studying lifelike 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 toward a distant target. By combining renewal-based intermittent motion with the Cramér-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 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.