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Related Experiment Video

Updated: Jun 27, 2025

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

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Nonreciprocity and odd viscosity in chiral active fluids.

Tomer Markovich^1,2, Tom C Lubensky³

¹School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel.

Proceedings of the National Academy of Sciences of the United States of America

|May 3, 2024

Summary

Odd viscosity in chiral active matter breaks Onsager reciprocal relations due to angular momentum density. This leads to new mechanical waves and potential nonreciprocal phase transitions.

Keywords:

active matter chiral active matter nonequilibrium statistical mechanics nonreciprocal active matter odd viscosity

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Area of Science:

Condensed matter physics
Active matter physics
Fluid dynamics

Background:

Odd viscosity couples stress and strain rate dissipationlessly.
Previously studied in plasmas, superfluids, and quantum-Hall fluids, often obeying Onsager reciprocal relations.
Its behavior in active materials, particularly chiral active matter, remains less understood.

Purpose of the Study:

To investigate whether Onsager reciprocal relations hold for odd viscosity in chiral active matter.
To explore the consequences of breaking these relations on material dynamics.
To identify conditions for the propagation of odd mechanical waves and mechanical instabilities.

Main Methods:

Direct coarse-graining of kinetic energy.
Application of the Poisson-bracket formalism.
Kinetic theory derivation.

Main Results:

Nonvanishing angular momentum density in chiral active matter breaks Onsager reciprocal relations.
This results in a non-Hermitian dynamical matrix and odd viscosity.
Identified regions for 3D odd mechanical wave propagation and mechanical instability, separated by exceptional points.

Conclusions:

Angular momentum density is key to breaking Onsager relations in active matter.
Odd viscosity and non-Hermitian dynamics arise from this breaking.
The findings suggest a possible nonreciprocal phase transition in chiral active materials.