A gas of ordinary, inert particles follows the familiar ideal gas law, linking pressure to density and temperature. Physicists at Heinrich-Heine University Düsseldorf (HHU), working with colleagues at the Technical University of Darmstadt, Sapienza University of Rome, and the University of Camerino, asked whether that same law holds for “active” particles that propel themselves and operate out of thermal equilibrium, publishing their analysis in the Proceedings of the National Academy of Sciences.

The team, led by Professor Hartmut Löwen, focused on “chiral” active particles, which move in circular orbits rather than straight lines — a pattern seen in swimming algae, rotating acacia seeds, and magnetically driven colloidal particles already being explored for adjustable shock absorbers. “The answer to this question is both yes and no,” Löwen said: the particles’ pressure still follows a form similar to the ideal gas law, but, he explained, “we can make the interpretation that an effectively higher temperature exists in the non-equilibrium state.”

When a spinning particle collides with a wall, its self-propulsion adds to the pressure it exerts, while its tangential motion along the surface partly cancels that effect out. The resulting equation of state depends on a handful of particle properties but, notably, not on the properties of the wall itself. That tangential motion also drives a directed flow of particles along the system’s edges — a behavior lead author Caprini said “represents an analogy to so-called topological insulators,” materials that conduct electricity only along their surfaces.

The team confirmed the theoretical predictions experimentally using chiral mini-robots built at HHU. Doctoral researcher Musacchio said, “Our experimental setup replicates the rotating systems to optimum effect,” and co-author Liebchen suggested the edge currents could eventually be harnessed to create flow fields that “enable the efficient transport of e.g. drugs,” efficiently and only at the boundaries of a system.

Endnotes

1. L. Caprini, H. Löwen, et al., “Active thermodynamics of inertial chiral active gases: equation of state and edge currents,” Proceedings of the National Academy of Sciences, July 17, 2026, DOI: 10.1073/pnas.2532158123.
2. Heinrich-Heine University Düsseldorf, “Thermodynamics of spinning particles,” news release via EurekAlert!, July 27, 2026.