Information bound on navigation speed in smart active matter

TL;DR

An adaptive active particle model that uses minimal information processing capabilities in order to navigate towards a distant target is introduced and a bound on the navigation speed valid for a wide range of information processing strategies is derived.

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 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 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.

Figures (3)

• Figure 1: Active agents use an intermittent navigation strategy that relies on information acquired during statistically independent periods to episodically reorient, generating a drift in a target direction. The $n$'th independent epoch is characterized by an initial orientation $\hat{n} [\hat{\theta}(\tau_{n-1})]$ based on information from the previous epoch, after which the particle performs normal active Brownian motion for a time $\tau_n$ while collecting information at a rate $\dot I\geq 0$.
• Figure 2: a) Cramér-Rao bound for the navigation speed for two different values of the information per persistence time. Solid line shows a deterministic renewal strategy, while the dashed line a stochastic one. b) Phase diagram where deterministic vs. stochastic strategies maximize the possible navigation speed, as function of mean renewal time and information gained.
• Figure 3: a) Cramér-Rao bound for the navigation speed without ($\mathcal{D}=0$) and with $(\mathcal{D} = 5)$ deterioration of the data before inference. Solid lines show deterministic renewal strategies, while the dashed line corresponds to Poissonian renewal times. The dimensionless information rate is set to $\dot{I}/D_r = 5$. b) Crossovers between optimal strategies.