The past decades have witnessed the flourishing of non-Hermitian physics in non-
conservative systems, leading to unprecedented phenomena of unidirectional invisibility …

A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

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 …

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-
reaching physical consequences observable in a range of dissipative settings are reviewed …

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 …

Active crystals are highly ordered structures that emerge from the self-organization of motile
objects, and have been widely studied in synthetic, and bacterial, active matter. Whether …

Non-reciprocal transmission of motion is potentially highly beneficial to a wide range of
applications, ranging from wave guiding to shock and vibration damping and energy …

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

Pair interactions between active particles need not follow Newton's third law. In this work, we
propose a continuum model of pattern formation due to nonreciprocal interaction between …