Complex Physical Systems

Complex physical systems encompass assemblies of many interacting components whose collective behaviour cannot be inferred simply from the properties of individual parts. Such systems often operate far from thermodynamic equilibrium, giving rise to emergent phenomena including spontaneous pattern formation, critical transitions and non-linear transport. Examples range from self-propelled colloids and active gels to turbulent flows and supercritical fluids, as well as magnetic avalanches and disordered elastic media. Across these contexts common themes recur: driving forces that sustain steady states, feedback loops that amplify or stabilise fluctuations, and networks of transient interactions that endow the system with both robustness and adaptability. Progress in this field has relied on the interplay of theory, computation and experiment to reveal universal scaling laws, identify new dynamical phases and devise principles for controlling or harnessing complex behaviour in materials, biological assemblies and engineered devices.

Research from Nature Portfolio

Photochromic swarms of colloidal particles have been realised by encoding distinct light-sensitive dyes on TiO₂ colloids and illuminating them with tailored wavelengths. This enables reversible gelation and phase segregation on demand, producing dynamic, colour-changing assemblies that respond adaptively to incident light. In a separate advance, the concept of active matter has been extended to proliferating systems in which particle number is not conserved: here birth, death and replication processes combine with self-propulsion to generate collective dynamics beyond those of fixed-size suspensions, suggesting new universality classes for growing and dividing assemblies. Complementing these soft-matter studies, supercritical fluids have been reinterpreted as complex networks of energetically localised molecular clusters. A hidden-variable network model reproduces both structural correlations and macroscopic response functions, revealing self-similar scaling in cluster size and connectivity across the extended supercritical regime and offering a unifying framework for solvent-mediated processes at high temperature and pressure.

Research from all publishers

In the realm of self-assembly, chiral photonic crystals have been engineered by programming colloidal patchy spheres to form single-network gyroid architectures. Two distinct patch designs yield enantiomorphic gyroid lattices with complete photonic bandgaps, demonstrating bottom-up routes to optical materials with rich chiroptical properties. On the frontiers of fluid turbulence, one-dimensional numerical experiments with the Majda–McLaughlin–Tabak model have rigorously tested the weak turbulence theory in the kinetic limit, confirming convergence to the Kolmogorov–Zakharov spectrum and recovering theoretical constants to high precision as nonlinearity vanishes and domain size grows. Finally, a mechanistic model has linked heterogeneous cluster dynamics in supercritical fluids to nonlinear thermodynamic anomalies: by partitioning energy exchange into contributions from cluster density changes, inter-cluster separation and molecule transfer, the theory accounts quantitatively for peaks in isobaric heat capacity and other response functions along the liquid-to-gas crossover.

Complex Physical Systems publication trend

The graph below shows the total number of articles in complex physical systems across all publications each year (not limited to Nature Index journals).

Technical terms

Non-equilibrium system: A system driven by sustained inputs or gradients that prevent relaxation to a conventional thermodynamic equilibrium.

Active matter: An assembly of units that consume energy locally to generate persistent motion or stresses, leading to collective phenomena such as swarming or phase separation.

Motility-induced phase separation: Spontaneous demixing of self-propelled particles into dense and dilute phases due to persistent motion and crowding, without attractive interactions.

Supercritical fluid: A state of matter beyond its critical temperature and pressure, exhibiting continuous transitions between liquid-like and gas-like behaviour.

Kolmogorov–Zakharov spectrum: A power-law distribution of wave energy across scales characterising the inertial cascade in weak wave turbulence.

Widom line: The locus of maxima in thermodynamic response functions extending beyond the critical point into the supercritical region, marking a continuous liquid-to-gas crossover.

References

1. Photochromism from wavelength-selective colloidal phase segregation. Nature (2023).
2. Proliferating active matter. Nature Reviews Physics (2023).
3. Supercritical fluids behave as complex networks. Nature Communications (2023).
4. Programmed Self‐Assembly of Single Colloidal Gyroids for Chiral Photonic Crystals. Advanced Materials (2023).
5. Verification of wave turbulence theory in the kinetic limit. Physical Review Research (2024).
6. Heterogeneous Cluster Energetics and Nonlinear Thermodynamic Response in Supercritical Fluids. Physical Review Letters (2024).