Bose-Einstein Condensation in the Framework of $κ$-Statistics

Abstract

In the present work we study the main physical properties of a gas of $κ$-deformed bosons described through the statistical distribution function $f_κ=Z^{-1}[\exp_κ(β({1/2}m v^2-μ))-1]^{-1}$. The deformed $κ$-exponential $\exp_κ(x)$, recently proposed in Ref. [G.Kaniadakis, Physica A {\bf 296}, 405, (2001)], reduces to the standard exponential as the deformation parameter $κ\to 0$, so that $f_0$ reproduces the Bose-Einstein distribution. The condensation temperature $T_c^κ$ of this gas decreases with increasing $κ$ value, and approaches the $^{4}He(I)-^{4}He(II)$ transition temperature $T_λ=2.17K$, improving the result obtained in the standard case ($κ=0$). The heat capacity $C_V^κ(T)$ is a continuous function and behaves as $B_κT^{3/2}$ for $T T_c^κ$, in contrast with the standard case $κ=0$, it is always increasing. Pacs: 05.30.Jp, 05.70.-a Keywords: Generalized entropy; Boson gas; Phase transition.