  Out of equilibrium phases of matter exhibiting order in individual
eigenstates, such as many-body localised spin glasses and discrete time
crystals, can be characterised by inherently dynamical quantities such as
spatiotemporal correlation functions. In this work, we introduce dynamical
potentials which act as generating functions for such correlations and capture
eigenstate phases and order. These potentials show formal similarities to their
equilibrium counterparts, namely thermodynamic potentials. We provide three
representative examples: a disordered, many-body localised XXZ chain showing
many-body localisation, a disordered Ising chain exhibiting spin-glass order
and its periodically-driven cousin exhibiting time-crystalline order.
