In classical or quantum systems in thermal equilibrium the interactions between degrees of freedom are fundamentally symmetric or reciprocal, a statement dictated by Newton’s third law and that in the quantum domain comes hand in hand with unitarity. Far from equilibrium however non-reciprocal interactions happen to be more the rule than the exception. Examples include optics, active matter, ecology and recently quantum systems. Non-reciprocity emerges naturally within non-Hermitian quantum mechanics, such as in the celebrated Hatano-Nelson model of particles hopping across a lattice with hopping different rates along opposite directions, and lead to a plethora of exotic topological and non equilibrium phenomena. The goal of this project is to explore the consequences of non-reciprocity on the dynamics of quantum many-body systems. Examples include the study of transport entanglement and phase transitions in presence of non-reciprocal couplings, in paradigmatic models of quantum many-body systems such as quantum spin chains or strongly correlated quantum impurity models.