Nonextensive Entropy of Quantum Liquid in Fractal Dimension Space

Superfluid hydrodynamic in fractal dimension space

“…where V represents potential energy. Suppose that velocity is more general quantity than momentum [16], one can rewrite (8) in terms of velocity and leave only the first spatial derivation of potential V . From fractional Schrodinger equation the mass conservation law follows in the form ∂ρ(r, t) ∂t + ∇J(r, t) + K(r, t) = 0,…”

“…Instead of parametr D α we introduce a new one with dimension of velocity as αD α = v 2−α 0 m 1−α . Then dynamic equation (8) for the superfluid component with taking into account thermodynamic relations [9] can be rewritten as…”

“…So one has to apply a new physics to describe such systems with taking into account their complex nature. For example, last two years the attempts to develop the fractionalized two-fluid hydrodynamics for nanoporous media with fractal dimensions have been made [7,8].…”

Quantum fluids in nanoporous media—Effects of the confinement and fractal geometry

“…So one has to apply new physics to describe such systems with taking into account their complex nature. For example, last two years the attempts to develop the fractionalized two-fluid hydrodynamics for nanoporous media with fractal dimensions have been made [9,10]. The actuality of such new hydrodynamics becomes very clear because of numerous studies of quantum liquids inside nanoporous media [11,12] as well as because of last developments in chemical synthesis of aerogels with different network of strands (from fibrous to globular one [13]).…”

“…The actuality of such new hydrodynamics becomes very clear because of numerous studies of quantum liquids inside nanoporous media [11,12] as well as because of last developments in chemical synthesis of aerogels with different network of strands (from fibrous to globular one [13]). One of the interesting obtained results is that density waves (the first sound) and temperature waves (the second sound) become strongly coupled even in the absence of viscosity, so it is purely geometric effect of fractal space of nanopores [9,10].In this paper we will review the procedure, results and discuss the issues for this approach. …”