Nonreciprocity and odd viscosity in chiral active fluids

TL;DR

This paper investigates how chiral active fluids exhibit nonreciprocal odd viscosity due to broken Onsager relations, leading to unique wave propagation and stability properties with potential non-reciprocal phase transitions.

Contribution

It demonstrates that angular momentum density in active fluids breaks Onsager reciprocity, resulting in non-Hermitian dynamics and the emergence of odd viscosity in these systems.

Findings

Nonreciprocal odd viscosity arises in chiral active fluids.

Regions of stable and unstable odd mechanical waves are identified.

Exceptional points mark phase transition boundaries.

Abstract

Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid ${\rm He}^3$, quantum-Hall fluids, and recently in the context of chiral active matter. In most of these studies, odd terms in the viscosity obey Onsager reciprocal relations. Although this is expected in equilibrium systems, it is not obvious that Onsager relations hold in active materials. By directly coarse graining the kinetic energy and independently using both the Poisson-bracket formalism and a kinetic theory derivation, we find that the appearance of a non-vanishing angular momentum density, which is a hallmark of chiral active materials, necessarily breaks Onsager reciprocal relations. This leads to a non-Hermitian dynamical matrix for the total hydrodynamic momentum and to the appearance of odd viscosity and other non-dissipative contributions to the viscosity. Furthermore, by accounting for both the angular momentum density and interactions that lead to odd viscosity, we find regions in the parameter space in which 3D odd mechanical waves propagate and regions in which they are mechanically unstable. The lines separating these regions are continuous lines of exceptional points, suggesting a possible non-reciprocal phase transition.