Elasticity typically refers to a material's ability to store energy, whereas viscosity refers to a
material's tendency to dissipate it. In this review, we discuss fluids and solids for which this is …

In active matter systems, individual constituents convert energy into non-conservative forces
or motion at the microscale, leading to morphological features and transport properties that …

Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity
occurs, for instance, in active matter,,,,–, non-equilibrium systems,–, networks of neurons …

In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes
that the rotation of constituent 'atoms' is determined by the flow and that viscous stresses …

We study the hydrodynamics of fluids composed of self-spinning objects such as chiral
grains or colloidal particles subject to torques. These chiral active fluids break both parity …

Chiral active matter comprises particles which can self-propel and self-rotate. Examples
range from sperm cells and bacteria near walls to autophoretic L-shaped colloids. In this …

Active particles contain internal degrees of freedom with the ability to take in and dissipate
energy and, in the process, execute systematic movement. Examples include all living …

Active materials are characterized by continuous injection of energy at the microscopic level
and typically cannot be adequately described by equilibrium thermodynamics. Here we …

Biological organisms and artificial active particles self-organize into swarms and patterns.
Open questions concern the design of emergent phenomena by choosing appropriate forms …

Fluids in which both time reversal and parity are broken can display a dissipationless
viscosity that is odd under each of these symmetries. Here, we show how this odd viscosity …