A. Aliano | Searcharxiv

arXiv2005

Maxwell-Juttner distributions in relativistic molecular dynamics

In relativistic kinetic theory, which underlies relativistic hydrodynamics, the molecular chaos hypothesis stands at the basis of the equilibrium Maxwell-Juttner probability distribution for the four-momentum $p^α$. We investigate the possibility of validating this hypothesis by means of microscopic relativistic dynamics. We do this by introducing a model of relativistic colliding particles, and studying its dynamics. We verify the validity of the molecular chaos hypothesis, and of the Maxwell-Juttner distributions for our model. Two linear relations between temperature and average kinetic energy are obtained in classical and ultrarelativistic regimes.

cond-mat.stat-mech↗

arXiv2002

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

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.

cond-mat.stat-mech↗