  We review current understanding of the non-equilibrium dynamics of collective
quantum systems. We describe an approach based on the Hamiltonian formulation
of superfluid hydrodynamics. It is shown that, in the presence of constant
energy pumping, the nonlinear coupling of fluctuations in the density and
entropy strongly affects the nonequilibrium dynamics of the system. We use the
results obtained to analyze the properties of out-of-equilibrium superfluid 4He
and of exciton polariton Bose-Einstein condensates, both in semiconductor
quantum wells and in graphene layers in presence of high magnetic field.
