Non-Gaussian statistics, maxwellian derivation and stellar polytropes

In this letter we discuss the Non-gaussian statistics considering two aspects. In the first, we show that the Maxwell's first derivation of the stationary distribution function for a dilute gas can be extended in the context of Kaniadakis statistics. The second one, by investigating the stellar system, we study the Kaniadakis analytical relation between the entropic parameter $\kappa$ and stellar polytrope index $n$. We compare also the Kaniadakis relation $n=n(\kappa)$ with $n=n(q)$ proposed in the Tsallis framework.Comment: 10 pages, 1 figur

Physical constraints on interacting dark energy models

Physical limits on the equation-of-state (EoS) parameter of a dark energy component non-minimally coupled with the dark matter field are examined in light of the second law of thermodynamics and the positiveness of entropy. Such constraints are combined with observational data sets of type Ia supernovae, baryon acoustic oscillations and the angular acoustic scale of the cosmic microwave background to impose restrictions on the behaviour of the dark matter/dark energy interaction. Considering two EoS parameterisations of the type $w = w_0 + w_a\zeta(z)$, we derive a general expression for the evolution of the dark energy density and show that the combination of thermodynamic limits and observational data provide tight bounds on the $w_0 - w_a$ parameter space.Comment: 7 pages, 4 figures. Accepted for publication in European Physical Journal

On the rotation of ONC stars in the Tsallis formalism context

The theoretical distribution function of the projected rotational velocity is derived in the context of the Tsallis formalism. The distribution is used to estimate the average for a stellar sample from the Orion Nebula Cloud (ONC), producing an excellent result when compared with observational data. In addition, the value of the parameter q obtained from the distribution of observed rotations reinforces the idea that there is a relation between this parameter and the age of the cluster.Comment: 6 pages, 2 figure