<p>On this paper the authors study the behavior of Superfluid Helium 4 near and below the Lambda line deriving its partition function and connecting and viewing the behaviors of the superfluid through a thermodynamic scope to&nbsp;give a better understanding from the perspective of applications and engineering. A great difficulty when dealing with superfluids is the need to understand some macroscopic behaviors through quantum events, which are challenging to describe and study within specific applications. For this reason, in this work a study of superfluids through a different scope is offered, where the microscopic phenomena are directly correlated to thermodynamic values typically used in applications and as such the transition to superfluidity can be viewed and studied through a thermodynamic and statistical point of view instead of a strictly quantum mechanical one. This process is initiated by deriving the partition function which is then split into an interacting and a non-interacting/ideal part. Hence, the models about the Bose-Einstein Condensation of an ideal Bose-Gas can be applied to the non-interacting/ideal part and then the results compared to the full superfluid, described by the quasiparticle approach. Thought the Bose function it is shown that the transition from the Bose-Einstein to the Maxwell-Boltzmann statistics in the non-interacting part is exhibited extremely near to the lambda transition of the actual superfluid Helium 4, 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 4. This scope of thinking about superfluidity, as well as offering the ability to study the superfluid transitions through a more understandable for an engineer point of view, it also has the significance of showing a mathematical connection of superfluidity to Bose-Einstein condensation. Overall, it seems that by the calculations 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 and being able to predict the macroscopical behaviors without the need of microscopic experimental data at regions where they are very difficult to be obtained.</p>

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

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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