Realistic scenario can be represented by general canonical ensemble way better than the ideal one, with proper parameter sets involved. We study the Bose-Einstein condensation phenomena of liquid helium within the framework of Tsallis statistics. With a comparatively high value of the deformation parameter $q(\sim 1.4)$, the theoretically calculated value of the critical temperature($T_c$) of the phase transition of liquid helium is found to agree with the experimentally determined value ($T_c = 2.17~\rm{K}$), although they differs from each other for $q=1$ (undeformed scenario). This throws a light on the understanding of the phenomenon and connects temperature fluctuation(non-equilibrium conditions) with the interactions between atoms qualitatively. More interactions between atoms give rise to more non-equilibrium conditions which is as expected.
\noindent {{\bf Keywords}: Tsallis statistics, Bose-Einstein condensation, liquid helium.}
Bose-Einstein condensation and the $λ$-transition are described in molecular detail for bosons interacting with a pair potential. New phenomena are identified that are absent in the usual ideal gas treatment. Monte Carlo simulations of Lennard-Jones helium-4 neglecting ground momentum state bosons give a diverging heat capacity approaching the transition. Pure permutation loops give continuous growth in the occupancy of the ground momentum state. Mixed ground and excited momentum state permutation loops give a discontinuous transition to the condensed phase. The consequent latent heat for the …
