An extensive study of Bose–Einstein condensation in liquid helium using Tsallis statistics

Abstract

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(∼ 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 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.

On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases

“…Phase transitions of systems obeying modified statistics have been studied particularly for generalized q-statistics in [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], where the corresponding critical condensation temperature has also been calculated [29]. An extended study of the thermodynamic properties presented in this work and other interesting ones will be reported elsewhere.…”

“…We will follow this path in order to estimate the critical temperature where the Bose condensation occurs for a quantum system characterized by the generalized statistics depending only on the probability [12,14]. This analysis has already been considered for the quantum statistics of q-generalized entropies, and quite interesting results arise [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. This particular result will also be explored here for other generalized entropies.…”

Constraints on light Dark Matter fermions from relic density consideration and Tsallis statistics

“…For more discussion related to this and to find its various applications please refer to [7,[20][21][22][23][24][25][26][27][28].…”

“…Note that the effective Boltzmann factor x i = (1 + (q − 1)bE i ) − 1 q−1 approaches to the ordinary Boltzmann factor e −bE i (= e −β 0 E i ) as q → 1. For more discussion related to this and to find its various applications please refer to [7,[20][21][22][23][24][25][26][27][28].…”

“…Using the Raffelt's criteria of the supernova energy loss rate for any new physics channel, we constrained the scale Λ of the dark matter effective theory [7]. Now in a realistic scenario, since the core temperature of the supernova is fluctuating, we worked within the formalism of Tsallis statistics [7,[19][20][21] where this temperature fluctuation is taken into account.…”