Unraveling the Landau's consistence criterion and the meaning of interpenetration in the 'Two-Fluid' Model

3 pags.
In this letter, we show that it is possible to unravel both the physical origin of the Landau’s consistence criterion and the specific and subtle meaning of interpenetration of the “two fluids” if one takes into account that in the hydrodynamic regime one needs a coarse-graining in time to bring the system into local equilibrium. That is, the fuzziness in time is relevant for the phenomenological Landau’s consistency criterion and the meaning of interpenetration. Note also that we are not questioning the validity of the “Two-Fluid” Model.
We gratefully thank Prof. C.F. Barenghi, Prof. T. Kodama and Prof. A.J. Leggett for correspondence exchange and Prof. A. Cruz for very illuminating discussions. In addition, Prof. Kodama has helped us to complete our knowledge about the hydrodynamic regime and without the help of Prof. Barenghi we would not have got all the content of his works, essential for the discussion in Section 3. We also acknowledge the referee's recommendations. This work was supported by Diputacion General de Aragon (Spain)-FSE Grants E24/2 and E24/3 and by Ministerio de Economia y Competitividad (Spain) Grants FIS2017-82426-P and FPA2015-65745-P. FA is supported by the DGA/European Social Fund Grant C070/2014.