Studying the Superfluid Transformation in Helium 4 Through the Partition Function and Entropic Behavior

Abstract

Abstract On this paper the authors study the behavior of Superfluid Helium 4 near and below the Lambda line deriving its partition function. The partition function is split into an interacting and a non-interacting/ideal part. Hence, the models about the Bose-Einstein Condensation of an ideal Bose-Gas are applied to the non-interacting/ideal part and then the results compared to the full superfluid, described by the quasiparticle approach. The transition from the Bose-Einstein to the Maxwell-Boltzmann statistics in the non-interacting part is exhibited extremely near the lambda transition of the actual superfluid Helium, hinting the effect of superfluidity in the ideal part of the system. Thus, the complete statistical model is now designed and calibrated by the known experimental data for its interacting part. With this model, since it is a theoretical method based on the partition function and entropy, not on the energy values of the quasiparticles, there is no theoretical limit to the lowest temperatures it can possibly describe. This entropic approach when extended well below the lambda-line, going near absolute zero, predicts the existence of an interatomic potential even at absolute zero, something that has been known to be the case for superfluid Helium. Overall, it seems that by the calculation of the authors the behaviors of superfluidity can also be observed and derived by studying the macroscopic variables, being the partition function and entropy in this way, thus offering a view of the superfluidity of the system through a different more macroscopical scope.