Thermodynamics Explained for Spinning Particles

Self-propelled “active” particles—microscopic objects that move by internally generating motion—have long challenged the classical picture of thermodynamics. A new study from Heinrich Heine University Düsseldorf (HHU), the Technical University of Darmstadt, Sapienza University in Rome, and the University of Camerino addresses a core question: does the familiar ideal-gas-like relationship between pressure, density, and temperature survive outside equilibrium? The work appears in Proceedings of the National Academy of Sciences (PNAS) and focuses on chiral active particles, which follow systematic circular trajectories rather than straight-line paths.

In equilibrium, gas pressure arises from the average force that particles transfer to a confining wall during collisions and reflections. Higher temperature means faster particles and therefore stronger impulses, leading to greater pressure. But active matter lives in a non-equilibrium world, where continuous self-propulsion and persistent motion complicate any direct mapping onto thermal concepts. Lead author Lorenzo Caprini and colleagues show that the answer is nuanced: the ideal-gas law no longer applies in a strict sense, yet an effective thermodynamic interpretation still emerges.

The team analyzes chiral microswimmers that repeatedly orbit while pushing against boundaries. Two wall-related mechanisms reshape the force balance. First, the particles’ self-propulsion contributes an “active swim pressure,” raising the normal stress at the surface. Second, chirality forces tangential motion along the wall, which partially offsets the normal contribution and modifies how momentum is redistributed near the boundary.

Remarkably, the researchers derive an equation of state in which the pressure depends on only a limited set of parameters, remaining largely insensitive to detailed wall properties. In practical terms, the non-equilibrium state can be described as if it possessed an activity-dependent effective temperature. “It resembles the ideal gas law but with an activity-dependent, effectively higher temperature,” notes HHU’s Hartmut Löwen, emphasizing why an equation of state can exist at all for driven systems.

Beyond pressure, the study predicts localized edge currents: tangential wall motion organizes particle flow near boundaries into directed currents. These currents provide a quantitative analog to concepts from topological insulator physics, where transport is constrained to system surfaces rather than filling the bulk. Such boundary-dominated behavior suggests a route to precisely targeted transport using active matter.

To validate the theory, the researchers performed experiments with chiral mini-robots. Marco Musacchio coordinated the experimental design to reproduce rotating dynamics with sufficient control. The comparison between measurements and analytical predictions is reported as unusually successful, supporting the proposed effective-temperature framework and the emergence of edge currents.

Finally, the findings open a path to engineered flow fields that function only at edges—potentially useful for applications such as directing substances through microstructured environments. The work establishes a foundational step for non-equilibrium thermodynamics of inertial chiral active gases and offers a predictive toolkit for future device-level control.

Keywords

Thermodynamics; Soft matter physics