Generic far-away-from-equilibrium many-body dynamics involve entropy production and hence is thermodynamically irreversible. Near quantum critical points, an emergent conformal symmetry can impose strong constraints on entropy production rates and in some cases can completely forbid entropy production, which usually occurs for systems that deviate from quantum critical points. In this article, we illustrate how the vanishing entropy production near a quantum critical point results in reversible far-away-from-equilibrium dynamics at finite temperatures that is otherwise irreversible. Away from the quantum critical point, the quantum dynamics is damped, and our analysis directly relates the thermalization timescale to the hydrodynamic viscosity near quantum critical points with the dynamical critical exponent
z=2. We demonstrate how both controllable reversible and irreversible dynamics can be potentially studied in cold gas experiments using Feshbach resonances.
Koopmanism -- the spectral theory of dynamicalsystems -- reduces the study of dynamical properties of a classical or quantum system S to the spectral analysis of its Liouvillean L_S . By definition, the operator L_S implements the dynamics on a suitable representation of the observable algebra of S. Near thermal equilibrium,this representation can often be constructed explicitely. Recent developments have shown that, in this situation, spectral analysis becomes a powerful tool in the study of thermal relaxation processes. Far from thermal equilibrium, the explicit construction of stationary states and of the corresponding representations is usually not possible. Nevertheless, important physical properties of the system S can be obtained from a fairly simple mathematical analysis. In this work, I investigate entropy production in open systems driven away from equilibrium by thermodynamic forces.