TY - JOUR

T1 - Nonreciprocity and odd viscosity in chiral active fluids

AU - Markovich, Tomer

AU - Lubensky, Tom C.

N1 - Publisher Copyright:
© 2024 the Author(s). Published by PNAS.

PY - 2024/5/7

Y1 - 2024/5/7

N2 - Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid He3, 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 nonvanishing 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 nondissipative 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 nonreciprocal phase transition.

AB - Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid He3, 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 nonvanishing 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 nondissipative 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 nonreciprocal phase transition.

KW - active matter

KW - chiral active matter

KW - nonequilibrium statistical mechanics

KW - nonreciprocal active matter

KW - odd viscosity

UR - http://www.scopus.com/inward/record.url?scp=85192129816&partnerID=8YFLogxK

U2 - 10.1073/pnas.2219385121

DO - 10.1073/pnas.2219385121

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C2 - 38701120

AN - SCOPUS:85192129816

SN - 0027-8424

VL - 121

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

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

IS - 19

M1 - e2219385121

ER -