Smart Matter: Adaptive Materials

• Smart matter is a class of adaptive materials that embed sensing, actuation, computation, memory, and feedback-driven learning into their structure.
• It integrates multiple functions into a distributed system, enabling self-organization and real-time adaptation across robotic, chemical, and biological domains.
• Research in smart matter emphasizes programmable, learning-driven behavior to achieve autonomous regulation and efficient, scalable applications.

Smart matter denotes a class of material and material-like systems in which sensing, actuation, computation, communication, memory, and adaptation are embedded into the physical substrate or into locally interacting constituent agents. In current research, the term is used in several closely related ways: as a distributed, non-equilibrium material system whose sensing, computation, memory, and actuation are inseparably co-located and self-organize through internal feedback; as active matter coupled to explicit regulatory interactions; as robotic materials that integrate sensing, actuation, computation, and communication at the material level; and as nonequilibrium matter whose governing parameters are updated in real time by feedback and learning (Baulin et al., 11 Nov 2025, Levine et al., 2023, Correll et al., 2017, Dauchot, 7 Jul 2026). In algorithmic work on programmable matter, the same theme appears as large populations of locally interacting computational particles that reconfigure shape and perform distributed tasks under severe locality and memory constraints (Derakhshandeh et al., 2014).

1. Conceptual scope and terminological distinctions

A persistent feature of the literature is that “smart matter” is broader than classical “smart materials.” Conventional smart materials are described as single-function materials that passively change property $A$ in response to stimulus $B$, whereas Smart Matter is defined as a distributed, non-equilibrium material system whose sensing, computation, memory, and actuation functions are inseparably co-located in its physical substrate and self-organize through internal feedback (Baulin et al., 11 Nov 2025). In active-matter language, active matter consists of interacting constituents that each have their own access to energy sources, while smart matter arises when that active medium is coupled to explicit regulatory interactions such as sensors, feedback loops, and signal-transduction networks that steer the active components toward functional goals (Levine et al., 2023).

Research lineage	Defining emphasis	Representative source
Programmable matter	Locally interacting computational particles	(Derakhshandeh et al., 2014)
Robotic materials	Co-located sensing, actuation, computation, communication	(Correll et al., 2017)
Active/odd/smart matter	Governing parameters adapt through feedback and learning	(Dauchot, 7 Jul 2026)
Material-based intelligence	Computation is the material’s own dynamics	(Baulin et al., 11 Nov 2025)

The distinction from active matter is especially important. Active matter refers to assemblies whose constituents consume energy locally to drive steady currents, stresses, or flows. Odd matter extends active solids by allowing an antisymmetric part of the elastic response, so that nonconservative elastic couplings permit work extraction under cyclic strain. Smart matter goes further by making the governing parameters themselves plastic: interaction strengths, elastic moduli, and control policies are updated in real time by feedback and learning, so that function is not fully hardwired (Dauchot, 7 Jul 2026).

A second distinction concerns embodiment. In robotic-materials research, intelligence is not located in a separate controller but in a composite fabric that integrates sensors, actuators, processors, and communication links. Essential properties proposed for such materials are size-independence, self-similarity and bulk reconfigurability, and robustness under loss of individual elements (Correll et al., 2017). This suggests a family resemblance rather than a single canonical definition: smart matter consistently denotes systems in which function is materially distributed, locally instantiated, and history dependent.

2. Physical principles and mathematical formalisms

Several mathematical frameworks recur across the field. In active and odd matter, constitutive structure is central. A generic linear constitutive law is written as

$\sigma_{ij}=C_{ijkl}u_{kl},$

with a decomposition into symmetric and antisymmetric parts, $C^e_{ijkl}=C^e_{klij}$ and $C^o_{ijkl}=-C^o_{klij}$. In odd elasticity this becomes

$\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$

and the odd contribution permits

$\oint \sigma_{ij}du_{ij}\neq 0,$

i.e. net work extraction over a closed strain cycle (Dauchot, 7 Jul 2026). In active liquids, hydrodynamic descriptions use density $\rho(x,t)$ and polarization $p(x,t)$, with equations such as

$$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$

Smart matter adds slow dynamics for the parameters themselves. In reinforcement-learning form, a policy parameter can evolve as

$B$0

while in physical learning schemes a constitutive parameter can be updated by internal-variable dynamics such as

$B$1

The point is not only that the material moves or deforms, but that the laws governing motion and deformation also evolve (Dauchot, 7 Jul 2026).

A complementary formulation emphasizes far-from-equilibrium field dynamics and attractor structure. Material-based intelligence is described using reaction–diffusion-type equations,

$B$2

network-reservoir dynamics,

$B$3

and energy-landscape dynamics,

$B$4

Memory is represented either as metastable attractors or as slow parameters $B$5 that reshape the landscape, for example through $B$6 (Baulin et al., 11 Nov 2025).

Control-theoretic formalisms supply another layer. One illustrative state-space block writes

$B$7

where $B$8 denotes sensed variables and $B$9 a reference. In this perspective, smart matter is active matter augmented by regulatory interactions operating across multiple timescales, from fast signaling and local stabilization to slow adaptation (Levine et al., 2023). A plausible implication is that the field is not defined by any single substrate—chemical, mechanical, robotic, or colloidal—but by the coupling of nonequilibrium physics to embedded regulation.

3. Architectures and material embodiments

One major architectural lineage is “robotic materials,” in which sensing, actuation, computation, and communication are co-located at the material level (Correll et al., 2017). Proposed component analogies include sensorized “bone” measuring structural load, actuating “muscle” based on electro-active polymers or shape-memory alloys, tactile “skin” with distributed capacitive or piezo-vibration sensors, and distributed “brain” material executing consensus or pattern-generation algorithms. Classification schemes distinguish passive, sensing-only, sensing-plus-actuation, sensing-plus-computation, fully active, and networked variants, as well as layered, embedded-node, and gradient/hybrid organizations.

A chemically explicit embodiment is the “intelligent plasma” framework, where a low-temperature partially ionized gas contains a programmable chemical pathway network (CPN) that performs data processing, decision making, and actuation (Lin et al., 2021). The concentration vector $\sigma_{ij}=C_{ijkl}u_{kl},$0 evolves as a continuous-time Markov process: $\sigma_{ij}=C_{ijkl}u_{kl},$1 Here rate coefficients $\sigma_{ij}=C_{ijkl}u_{kl},$2 play a role analogous to tunable weights. The paper describes chemical implementations of “if” conditions and “while” loops, including an automatic atomic-layer etching workflow in which photon-gated release of $\sigma_{ij}=C_{ijkl}u_{kl},$3 regulates sidewall protection without external timing. Reported plasma collisional rates are $\sigma_{ij}=C_{ijkl}u_{kl},$4, with self-regulated cycle frequencies in the $\sigma_{ij}=C_{ijkl}u_{kl},$5 range (Lin et al., 2021).

A different embodiment is the hygromorph composite material machine built from Laywood™ meta-5 filament and carbon-black–reinforced PLA (Kergariou et al., 5 Jun 2026). Four identical hygromorph actuators are arranged in a “Quadruple Stacked Down-Facing” aperture; each actuator functions as a neuron whose bending angle encodes activation, while transmitted light is the network output. The surrogate neural network takes input $\sigma_{ij}=C_{ijkl}u_{kl},$6, control voltages $\sigma_{ij}=C_{ijkl}u_{kl},$7, and predicts internal illuminance $\sigma_{ij}=C_{ijkl}u_{kl},$8. The network is a single-layer fully connected feed-forward model with one hidden layer of $\sigma_{ij}=C_{ijkl}u_{kl},$9 neurons. The database contains more than 350 experiments, and incremental training yields $C^e_{ijkl}=C^e_{klij}$0 rising to $C^e_{ijkl}=C^e_{klij}$1 by 120 points while $C^e_{ijkl}=C^e_{klij}$2 plateaus around $C^e_{ijkl}=C^e_{klij}$3; $C^e_{ijkl}=C^e_{klij}$4 predictions lie within $C^e_{ijkl}=C^e_{klij}$5 of the true value (Kergariou et al., 5 Jun 2026). The actuators exhibit actuation strain typically $C^e_{ijkl}=C^e_{klij}$6, light-transmission variation greater than $C^e_{ijkl}=C^e_{klij}$7, and reversibility leveling to below $C^e_{ijkl}=C^e_{klij}$8 standard deviation after $C^e_{ijkl}=C^e_{klij}$9 cycles.

Shape-memory composite interfaces provide yet another route. The TSMP/M heterointerface combines a thermoplastic shape-memory polymer with selectively deposited metal layers through multi-material DLP printing and electroless plating (Song et al., 2023). The resulting three-layer cross section consists of a pure polymer layer, an intermediate composite layer of Ni nanoparticles embedded in the network, and a pure metal layer $C^o_{ijkl}=-C^o_{klij}$0 thick after 12 minutes of plating. Reported low-voltage actuation occurs at $C^o_{ijkl}=-C^o_{klij}$1; an Eiffel-Tower trace with $C^o_{ijkl}=-C^o_{klij}$2 recovers shape in $C^o_{ijkl}=-C^o_{klij}$3, lattice scaffolds in $C^o_{ijkl}=-C^o_{klij}$4 at $C^o_{ijkl}=-C^o_{klij}$5, and bending-peel tests exceed 100 cycles with less than $C^o_{ijkl}=-C^o_{klij}$6 resistance drift (Song et al., 2023). These systems integrate actuation, sensing, and electronic interfacing within a single printed heterointerface.

4. Biological and bio-inspired smart matter

Living systems furnish both exemplars and minimal models. In Physarum polycephalum, smart behavior is attributed to network adaptation in a tubular active poro–visco–elastic system (Verge-Serandour et al., 2023). A one-dimensional tube is modeled with gel displacement $C^o_{ijkl}=-C^o_{klij}$7, sol velocity $C^o_{ijkl}=-C^o_{klij}$8, pressure $C^o_{ijkl}=-C^o_{klij}$9, and active stress $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$0, using force balance, incompressibility, Darcy coupling, and reaction–diffusion–advection of a chemical oscillator: $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$1 Typical parameters reported are $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$2, $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$3, $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$4, and $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$5 for small ions. At network scale, a tube radius $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$6 adapts over tens of minutes to the local time-averaged shear rate $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$7, with a fitted adaptation time $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$8, delay time $\sigma_{ij} = K_{ijkl}u_{kl} + K^o_{ijkl}u_{kl},$9, and reference shear $\oint \sigma_{ij}du_{ij}\neq 0,$0 (Verge-Serandour et al., 2023).

The mature plasmodial network is described as a nearly planar, degree-three graph with log-normal tube radii and mean radius $\oint \sigma_{ij}du_{ij}\neq 0,$1. It obeys Murray’s law at three-way junctions,

$\oint \sigma_{ij}du_{ij}\neq 0,$2

and peristaltic waves of contraction span the entire network with $\oint \sigma_{ij}du_{ij}\neq 0,$3, producing shuttle streaming at $\oint \sigma_{ij}du_{ij}\neq 0,$4 and Womersley number $\oint \sigma_{ij}du_{ij}\neq 0,$5 (Verge-Serandour et al., 2023). The same review identifies multiple memory media: external slime-trail memory, network-architecture memory, dynamical-state memory under periodic stimulation, and long-lived chemical-composition memory transferred by fusion. It explicitly maps these to computing primitives such as external rewritable memory, distributed structural memory, phase-encoded logic, and concentration-encoded analog information.

Bio-inspired but synthetic and robophysical systems extend these ideas through entanglement. In amorphous entangled active matter, collections of concave three-link “smarticles,” robophysical chains, and living worm blobs are used to study shape-modulating materials (Savoie et al., 2022). The average entanglement is

$\oint \sigma_{ij}du_{ij}\neq 0,$6

and under tensile tests the peak force scales approximately linearly with entanglement density $\oint \sigma_{ij}du_{ij}\neq 0,$7, giving $\oint \sigma_{ij}du_{ij}\neq 0,$8. Three open-loop activation procedures are compared: external oscillation of the container, shape-change of each particle, and internal oscillations of each barb. Shape-change yields the highest average entanglement, up to $\oint \sigma_{ij}du_{ij}\neq 0,$9 at $\rho(x,t)$0; internal oscillations give optimal entanglement at $\rho(x,t)$1 when $\rho(x,t)$2; and internal oscillations have the lowest energy cost (Savoie et al., 2022).

Robophysical chains exhibit auxeticity under tension, with measured negative Poisson ratio $\rho(x,t)$3 to $\rho(x,t)$4. In living Lumbriculus variegatus worm blobs, ambient dissolved oxygen controls collective state: low DO $\rho(x,t)$5 produces weak entanglement and a fluid-like “melted” blob, whereas high DO $\rho(x,t)$6 produces strong entanglement and a solid-like blob (Savoie et al., 2022). These studies treat tunable morphology, mechanical response, and collective adaptation as material properties rather than as external control effects.

5. Programmable matter and self-organizing particle systems

A rigorous algorithmic branch of smart matter research studies programmable matter as very large numbers of locally interacting computational particles. In the Amoebot model, particles live on the infinite triangular lattice $\rho(x,t)$7, occupy either one node (“contracted”) or two adjacent nodes (“expanded”), and maintain constant-size state plus edge flags from finite alphabets (Derakhshandeh et al., 2014). They have no global identifiers and no global compass, but do possess local port numbering and shared chirality. Motion is generated by three primitives: expansion, contraction, and coordinated handover. The scheduler is asynchronous and fair: at each step some enabled locally non-conflicting action fires, and fairness prevents starvation.

Within this model, Derakhshandeh et al. analyze the infinite object coating problem. A fixed object occupies a connected compact subgraph $\rho(x,t)$8, all non-object particles begin contracted and inactive in a connected configuration, and the goal is a state where every non-object particle is contracted and adjacent to some object node (Derakhshandeh et al., 2014). The algorithm combines three primitives: surface motion by leaders adjacent to the object, a spanning-forest mechanism that turns inactive particles into followers and then leaders, and complaint propagation that terminates motion once coating is complete. The correctness theorem states that the system remains connected, terminates, and ends with every non-object particle contracted on the object’s surface. Work is defined as the total number of expand/contract moves, with a handover counted as 2, and the algorithm is work-optimal with

$\rho(x,t)$9

The same geometric amoebot framework has also been used for explicit distributed computation under $p(x,t)$0 memory per particle (Porter et al., 2017). A distributed binary counter arranges particles in a line adjacent to a seed; each particle stores a counter $p(x,t)$1, a display bit $p(x,t)$2, and constant-size token buffers. The counter requires $p(x,t)$3 particles to count to $p(x,t)$4 and takes $p(x,t)$5 asynchronous rounds (Porter et al., 2017). Matrix–vector multiplication is implemented by streaming a matrix into an $p(x,t)$6 particle grid and accumulating results in counter rows, with setup cost $p(x,t)$7 and multiplication cost $p(x,t)$8. The same system supports image-processing primitives: after grid setup in $p(x,t)$9, Canny/Sobel-style edge detection runs in $$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$0 asynchronous rounds, and color transformations are realized as three simultaneous matrix–vector multiplications (Porter et al., 2017).

This line of work is notable because it treats smart matter not merely as a responsive material but as a distributed computational medium with explicit complexity bounds, connectivity invariants, and asynchronous correctness guarantees. Applications named in the literature include smart paint, coating materials for engineering, and programmable cells for medical uses (Derakhshandeh et al., 2014, Porter et al., 2017).

6. Learning, information processing, and fundamental limits

A recent direction makes learning itself the constitutive principle. “From Active to Odd to Smart Matter” argues that smart matter is the next step beyond active and odd materials because the rules governing collective behavior become plastic, adapting and improving through experience (Dauchot, 7 Jul 2026). At the level of architecture, this introduces a fourth layer beyond design, programming, and feedback control: learning-driven adaptation, in which feedback signals reshape constitutive or decision-making rules themselves. In a related formalization of intelligent matter, the required functional components are sensing $$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$1, actuation $$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$2, memory $$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$3, and an internal information network $$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$4, so that internal state obeys $$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$5 with nontrivial memory and bidirectional coupling between sensing and actuation (Jeggle et al., 15 Dec 2025).

Machine learning enters smart active matter through both external and internal control architectures. Synthetic active particles may be controlled by an external loop,

$$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$6

or by on-board sensors, processor, and actuators (Löwen et al., 15 Jan 2025). The chapter on intelligent active particles formulates single-agent navigation using Q-learning, DQN, and actor–critic methods, and multi-agent cooperation using mean-field reinforcement learning. Typical parameters given for a microswimmer are $$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$7, $$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$8, $$\partial_t \rho+\nabla\cdot(\rho v)=0,\qquad \partial_t p+\lambda_1(v\cdot\nabla)p=-\delta F/\delta p+\ldots+f_{\mathrm{active}}.$$9, and $B$00; after training, path efficiency reaches $B$01, and cooperative learning yields a $B$02 boost in total nutrient uptake versus greedy chemotaxis (Löwen et al., 15 Jan 2025).

A more statistical-physical treatment is provided by the kinetic theory of decentralized learning for smart active matter (Jung et al., 7 Jan 2025). Each agent carries a physical state $B$03, memory $B$04, policy $B$05, and position $B$06, and the one-body density evolves according to

$B$07

Learning is modeled as a pairwise exchange process in which neighbors compare rewards and one copies the policy and memory of the higher-reward “teacher.” Under time-scale separation and Gaussian closure, the macroscopic mean policy $B$08 and diversity $B$09 obey closed equations of the form

$B$10

For phototactic microswimmers, the theory yields an uncertainty relation

$B$11

which expresses a trade-off between learning speed and residual diversity (Jung et al., 7 Jan 2025).

Information-theoretic and thermodynamic limits have also been derived. For a renewal-based adaptive active particle that periodically senses a target direction, the long-time drift speed toward the target is bounded by a Cramér–Rao-based expression,

$B$12

with explicit dependence on the renewal-time distribution $B$13, rotational noise $B$14, and total Fisher information $B$15 (Olsen et al., 27 Feb 2026). For deterministic sensing intervals and uniform information growth $B$16, the bound predicts an optimal sensing time $B$17 and a speed–accuracy trade-off between short, noisy measurements and long, decorrelating runs. Allowing memory decay lowers maximal speed but, to leading order, does not shift the optimal run time (Olsen et al., 27 Feb 2026). In a complementary stochastic-thermodynamic analysis of controlled active Brownian swimmers, the dissipation required for localization obeys

$B$18

for point-target localization, with analogous bounds for line-following (Cocconi et al., 2024). Perfect localization therefore requires divergent dissipation.

Open problems are explicit across the literature. They include integration of learning with nonequilibrium physics, coarse-graining of learning laws into effective field theories, universality classes of learning matter, emergent adaptation topologies, the choice between function-first and rule-first design, fault tolerance and self-healing, extension of programmable matter to 3D lattices, relaxation of compact-object assumptions, energy-aware motion, and moving computation fully into the material structure rather than into a digital surrogate (Dauchot, 7 Jul 2026, Derakhshandeh et al., 2014, Kergariou et al., 5 Jun 2026). Taken together, these directions define smart matter as an attempt to make materials and collectives not merely responsive, but self-organizing, adaptive, computational, and in some formulations explicitly learnable.