Non-equilibrium Thermodynamics of Superfluid Helium and Quantum Turbulence

David Jou has been professor of Condensed Matter Physics at the Autonomous University of Barcelona, Spain for forty years. His research interests deal with non-equilibrium thermodynamics and statistical physics, heat transport, superfluids, and nanosystems. He has published five research monographs, three hundred specialized papers, and eight scientific essays for the general public.Maria Stella Mongiovì was professor of Mathematical Analysis, Theoretical Mechanics and Mathematical Physics at the University of Palermo, Italy. Her research interests deal with non-equilibrium thermodynamics (rational and irreversible) with application to superfluids and other complex systems. She has published two hundred research papers and books, and several teaching contributions.Michele Sciacca is professor of Mathematical Analysis, Theoretical Mechanics and Mathematical Physics at the University of Palermo, Italy. His research interests deal with non-equilibrium thermodynamics applied to heat transport, superfluids and nanosystems; complete integrability of Partial Differential Equations; research of exact solutions in PDEs and in particular, travelling waves and solitons in complex systems.

• .- Introduction.- The two-fluid model of superfluid hydrodynamics.- The one-fluid extended model.- Superfluid hydrodynamics in rotating systems.- Turbulence in superfluids.- Coupled heat and vortex flows.- Coupling between mass flow, heat flux and vortices.- Microscopic approach to Helium II.- Quantized vortices.- Classical vs quantum turbulence.- Thermodynamics of vortex tangles and of cosmic strings.- Perspectives and suggestions.