Gaussian fluctuations of nonreciprocal systems

Nonreciprocal systems can be thought of as disobeying Newton's third law—an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest toward such systems. On a fundamental level, they can be a basis of describing nonequilibrium and active states of matter, with applications ranging from physics to social sciences. However, often the first step to understanding complex nonlinear models is to linearize about the steady states. It is thus useful to develop a careful understanding of linear nonreciprocal systems, similar to our understanding of Gaussian systems in equilibrium statistical mechanics. In this work we explore simplest linear nonreciprocal models with noise and spatial extent. We describe their regions of stability and show how nonreciprocity can enhance the stability of a system. We demonstrate the appearance of exceptional and critical exceptional points with the respective enhancement of fluctuations for the latter. We show how strong nonreciprocity can lead to a finite-momentum instability. Finally, we comment how nonreciprocity can be a source of colored, 1/f type noise.