Non-equilibrium Thermodynamics of Superfluid Helium and Quantum Turbulence

This book puts together non-equilibrium thermodynamics, heat transport properties of superfluid He II, and thermodynamic and dynamic aspects of quantum turbulence. A one-fluid extended model of superfluid helium, with heat flux as an additional independent variable, is presented and compared with the two-fluid model, to explore how both models complement each other. Important features arise in rotating situations and in superfluid turbulence, characterized by quantized vortices leading to strong nonlinearities between heat flux and temperature gradient. The dynamics of vortex lines and their interaction with heat dynamics, a central topic in superfluid turbulence, is dealt with by introducing the vortex line density as an independent variable and writing its dynamical equations, considering the transitions from laminar to turbulent flows and from diffusive to ballistic regimes. Classical and quantum turbulence are compared from a mesoscopic view and from their energy spectra.

The work also explores some parallelisms of quantum vortex thermodynamics with cosmic string thermodynamics and black-hole thermodynamics, exhibiting duality connections amongst them. It emphasizes didactical views over specialistic details, and may be used as an introduction to nonequilibrium thermodynamics of superfluid helium and its heat transport properties (second sound, nonlocal transport, nonlinear connections with quantum turbulence).

The book is useful to researchers in superfluid helium, in heat transport, and in thermodynamics of cosmic strings and black holes. The diversity and complexity of its several physical equations will be inspiring for researchers in mathematical physics.

Provides an overview of non-Fourier heat transport, hydrodynamic heat transfer, and nonlinear heat transfer Serves as a primer for graduate students in mathematical physics, and researchers in non-equilibrium thermodynamics Deals with duality connections between quantum vortices, cosmic string and black hole thermodynamics

Autorentext

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.

Inhalt

.- 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.