Non-reciprocal statistical physics in quantum, active, and biological matter

Processes fundamental to everyday experience — from activity in networks of neurons to evolution of ecosystem — operate far from equilibrium to sustain the dynamics essential for life, computation, and complex adaptive behavior. Non-reciprocal interactions provide a generic route to such nonequilibrium behavior: the influence of agent A on agent B differs from that of B on A. Neural circuits, ecosystems, chemical reaction networks, social interactions, and open quantum systems often realize this asymmetry such that rich collective dynamics can occur. In particular, non-reciprocity often leads to the emergence of persistent, time-dependent many-body phases driven by non-reciprocity. A distinctive feature of non-reciprocal phase transitions is that they may occur at critical exceptional points, where critical slowing down coincides with an existing zero mode associated with broken continuous symmetry. In this thesis, we explore the broad landscape of phases and phase transitions enabled by non-reciprocity. We are especially interested in how generalized exceptional points organize dynamics and response in non-equilibrium many-body systems, how geometry and boundary conditions reshape collective behavior in spatially extended non-reciprocal media, and how symmetry and topology constrain the possible time-dependent phases and critical phenomena in multi-population systems of interacting agents. Together, these results provide a framework for non-reciprocal phase transitions and motivate future tests across experimental settings.