Informational Active Matter

• Informational active matter is a class of nonequilibrium systems that couples energy transduction with feedback-driven information processing to direct agent behavior.
• Methodologies integrate kinetic, hydrodynamic, and computational models using feedback protocols that modify traditional collision and flow equations.
• Applications span programmable colloids to active flow networks that implement logic operations, paving the way for adaptive materials and novel control systems.

Informational active matter refers to a class of nonequilibrium active systems in which energy transduction at the microscale is intricately coupled to information processing, decision-making, or feedback–inspired protocols. In these systems, the individual elements—ranging from colloidal particles and cells to robots—do not merely react passively to stochastic fluctuations or deterministic forces, but actively process environmental or internal signals, store information, and utilize feedback to guide their interactions or motile behavior. The interplay between energetics, feedback control, and information leads to emergent, large-scale dynamics such as collective motion, pattern formation, robust coordination, and in some cases, physical computation or memory. Informational activity is manifest across biological collectives, programmable synthetic systems, and theoretically constructed feedback-powered engines, and it marks a fundamental extension of the active matter paradigm by embedding information as a first-class driver alongside energy.

1. Energetics, Microscopic Feedback, and Information Encoding

Informational active matter extends traditional active matter frameworks—where each agent locally consumes and dissipates energy—to encompass explicit measurement, feedback, and decision-making at the level of the agent (Menon, 2010, VanSaders et al., 2023, Yasuda et al., 15 Oct 2025). Energy is converted into useful work by self-propelled units, but crucially, the agents’ motility or interaction rules are conditional on local states or environmental signals. For example, in decision-driven protocols, agents gather information through measurements (such as relative velocity or local density) and adapt internal variables (diameter, orientation, propulsion force) according to stochastic or deterministic rules.

The information-theoretic characterization relies on quantifying the entropy (information) processed by these protocols, which can be made explicit using Markov chain modeling with transition probabilities $P_{ij}$ between discrete states, yielding a per-step information (VanSaders et al., 2023): $I = -\sum_{i,j} \mu_i P_{ij} \ln P_{ij}$ where $\mu_i$ denotes stationary probabilities. Landauer’s bound ties this information to thermodynamic cost: $\mathcal{W} \le k_BT I$ Feedback protocols can be nearly workless for vanishingly small bias amplitudes, but the information processed always bounds the extractable work or reduction in entropy.

In the informational Onsager-Machlup Principle (Yasuda et al., 15 Oct 2025), the path probability is conditioned on memory states, integrating the Rayleighian with respect to the measured outcomes: $$O[{\bf x}(t), {\bf v}(t), {\bf a}(t)| {\bf y}, {\bf x}_0] = \frac{1}{2k_BT} \int_{t_0}^{t_f} dt\,[R({\bf x},{\bf v},{\bf a}|{\bf y}) - R_*(\bf x,\bf a|{\bf y})]$$ This formalism unifies dissipative, energetic, and informational effects at the trajectory level.

2. Kinetic, Hydrodynamic, and Computational Models of Decision-Based Control

At the kinetic level, informational protocols are incorporated by modifying the Boltzmann collision operator for an agent’s velocity distribution $f(\vec{v}, t)$ (VanSaders et al., 2023): $$\frac{\partial f}{\partial t} = \mathcal{Q}(f) = \frac{1}{2} \int d\sigma \int d\vec{v}_*\, B(\sigma, \Delta \vec{v}) [\beta f(\vec{v}')f(\vec{v}_*') - f(\vec{v})f(\vec{v}_*)]$$ with $\beta \ne 1$ encoding the impact of feedback or information protocols (e.g., adaptive size selection to bias collision outcomes). This selective feedback induces phase-space compression and breaks microreversibility, resulting in macroscopic currents or collective order even when energy and momentum are microscopically conserved. The mean drift velocity for a “thinker” gas is controlled by higher-order moments: $$u_i = -\frac{m}{2k_BT} \int v_i\, |\vec{v}|^2 f_t(\vec{v})\, d\vec{v}$$

In coarse-grained hydrodynamic theories, information is encoded in local fields such as the density $c({\bf r}, t)$ and the orientational order parameter $P({\bf r}, t)$ (Menon, 2010). The evolution of these fields incorporates feedback–driven active stresses (cf. equation (2) in (Menon, 2010)) that couple local alignment to the propagation of “signals” through the fluid, enabling amplification and transport of local informational states.

Agent-based models, such as the Vicsek model, represent information transfer as alignment to local neighbors with a noise-perturbed rule: $$\theta_i(t+1) = \langle \theta_i(t) \rangle_R + \xi_i(t)$$ with $\langle \cdot \rangle_R$ denoting local averaging—an effective social or informational decision.

3. Feedback, Pattern Formation, and Self-Organization

Informational feedback is operationalized in both natural and synthetic active matter by real-time processing of sensory input to direct future behavior, which fundamentally modifies the character of emergent collective states (Hagan et al., 2016, Khadka et al., 2018, Falk et al., 2021, VanSaders et al., 2023).

Experimentally, programmable feedback loops have been realized in optically or electronically controlled active colloids (Khadka et al., 2018). The propulsion direction and interaction strength are dictated not by physical contact but by a real-time information loop, e.g.: $$v_i(t) = -v_{\text{th}}\cdot e_i(t), \qquad e_i(t) = \frac{\sum_{j \ne i} \text{sign}(r_{ij}(t-\delta t)-r_{\rm eq}) e_{ij}}{|\sum_{j \ne i} \text{sign}(r_{ij}(t-\delta t)-r_{\rm eq}) e_{ij}|}$$ with a tunable feedback delay $\delta t$. Such protocols drive the formation of structured “active molecules” that possess internal vibrational and reconfiguration modes determined by the algorithmic form of the information–based interaction.

A key feature is that informational feedback can lead to noise-induced patterning where increased environmental fluctuations (noise) enhance rather than degrade spatial order, in stark contrast to equilibrium intuition (VanSaders et al., 2023).

4. Computation, Memory, and Logic in Active Flow Networks

Beyond patterning and ordered motion, informational active matter demonstrates the ability to realize computation and memory through the physical organization of its flows. Active Matter Logic (AML) (Woodhouse et al., 2016) utilizes networks of microfluidic channels with spontaneous active flows—driven by bacterial suspensions, active nematics, or motile colloids—to implement Boolean logic and multistability.

Each network is abstracted as a graph $\Gamma = (V, E)$ with edge variables $\varphi_e \in \{-1, 0, 1\}$. The network energy is governed by a double-well Hamiltonian with incompressibility enforced at vertices: $$H_0 = \lambda \sum_{e \in E} V(\varphi_e) + \frac{1}{2}\mu \sum_{v \in V} (D \cdot \varphi)_v^2$$ Logic gates (AND, OR, NOT, NAND, Fredkin, and memory latches) are realized by geometric constraints, active flow selection, and conservation laws, providing a physical substrate for universal computation.

Non-locality and topological frustration deeply distinguish these logic networks from classical Turing machines; signal and information are embodied by flow states propagated and stabilized through self-organized selection of network ground states.

5. Thermodynamic Constraints and the Role of Noise

Energetic and informational constraints are tightly interlinked in informational active matter, manifested in both thermodynamic bounds and stochastic process control (Gaspard et al., 2020, Goerlich et al., 2021, Chatterjee et al., 22 Aug 2025, Yasuda et al., 15 Oct 2025).

Information harvesting protocols, such as those based on correlated (“colored”) noise baths (Goerlich et al., 2021), demonstrate control of nonequilibrium states via tuning of noise correlation times. The resulting heat cost is measured directly by the change in spectral entropy of the colored noise, in a form reminiscent of Landauer’s principle: $\Delta Q = k_B T_\text{eq} \Delta H_S$ with $H_S$ the spectral entropy of the noise bath.

Noisy active matter systems use energy-consuming feedback to rectify stochastic fluctuations, with noise acting as both a resource for adaptive order and a driver of symmetry breaking (Chatterjee et al., 22 Aug 2025). Feedback protocols are designed such that multiplicative, state-dependent noise enables transitions between metastable states, enhances exploration of configuration space, and robustly seeds emergent behavior despite environmental uncertainty.

6. Applications: Collective Control, Adaptive Materials, and Future Directions

Informational active matter underpins applications in micromanipulation, programmable self-organization, feedback-powered engines, and physical computation (Khadka et al., 2018, Woodhouse et al., 2016, Falk et al., 2021, Cai et al., 30 Mar 2025). Reinforcement learning (RL) schemes have been successfully employed to optimize tasks such as navigation, foraging, and even computation of optimal control laws for swarms—translating high-level objectives into spatiotemporal patterns of activity in noisy environments (Falk et al., 2021, Cai et al., 30 Mar 2025).

Programmable feedback at the level of active gels, cytoskeletal extracts, microrobotic swarms, or droplet–colloid “superstructures” enables dynamic functions beyond the reach of passive or purely energetic active materials, including adaptive memory, error correction via global feedback, and “smart” patterning.

A major future direction is the systematic design of feedback-powered devices that operate far from equilibrium, governed by the principles established in the informational Onsager-Machlup formalism (Yasuda et al., 15 Oct 2025), with applications in next-generation information engines, interactive matter, and robust adaptive materials.

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Table: Examples of Informational Protocols in Active Matter Systems

System / Protocol	Information Processing Mode	Emergent Function
Feedback-controlled colloids	Real-time position measurement; laser-directed propulsion	Assembly of active “molecules” with programmable geometry (Khadka et al., 2018)
Active Matter Logic networks	Mass-conserving, topologically constrained flow states	Universal Boolean gates; memory latches (Woodhouse et al., 2016)
Adaptive “thinker” gas	Measurement-guided state switching (diameter/velocity)	Noise-induced flocking, pattern sharpening (VanSaders et al., 2023)
Light-controlled Vicsek system	RL-trained spatiotemporal activity patterns	Net transport; flocking control (Falk et al., 2021)
Feedback-modulated swimmer	Velocity measurement and drag switching in feedback	Persistent directional motion; information engine (Yasuda et al., 15 Oct 2025)

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The informational active matter framework provides a unifying organizational principle whereby self-propelled agents harness information flows, via feedback and environmental sensing, to drive complex far-from-equilibrium dynamics. Through an overview of energetic, hydrodynamic, computational, and thermodynamic models, informational activity offers robust strategies for control, adaptation, and the emergence of macroscale function in both biological and artificial matter.