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We consider a thermal particle which is diffusing in velocity-space and in a weakly confining potential characterized by the inverse hyperbolic sine function of the particle velocity $v$ and the control parameter $v_c$. The stationary state…
We study the long-time behavior of the $\kappa$-Markov local-field equation ($\kappa$-MLFE), which is a conditional McKean-Vlasov equation associated with interacting diffusions on the $\kappa$-regular tree. Under suitable assumptions on…
It is shown phenomenologically that the fractional derivative $\xi=D^\alpha u$ of order $\alpha$ of a multifractal function has a power-law tail $\propto |\xi| ^{-p_\star}$ in its cumulative probability, for a suitable range of $\alpha$'s.…
We consider a dilute quantum gas of interacting spin-1/2 fermions in the thermodynamic limit. For a trial state that resolves the ground state energy up to the precision of the Huang--Yang formula, we rigorously derive its momentum…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…
Anomalous diffusion and non-Gaussian statistics are detected experimentally in a two-dimensional driven-dissipative system. A single-layer dusty plasma suspension with a Yukawa interaction and frictional dissipation is heated with laser…
In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a non-thermal power-law tail at high energies. We argue that turbulence with initially…
We performed event-driven simulations of a two-dimensional granular gas between two vibrating walls and directly measured the local heat flux and energy dissipation rate in the stationary state. Describing the local heat flux as a function…
When the Zeeman energy approaches the characteristic kinetic energy of electrons, Landau quantization becomes important. In the vicinity of magnetars, the Zeeman energy can even be relativistic. We start from the Dirac equation and derive a…
We present a theoretical study of the compressibility, $\kappa$, in a Fermi gas with attractive contact interactions, providing predictions for the strongly-attractive regime and the superfluid phase. Our work emphasizes the compressibility…
We consider the quantization of a scalar kappa-deformed field up to the point of obtaining an expression for its vacuum energy. The expression is given by the half sum of the field frequencies, as in the non-deformed case, but with the…
We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential depending on the distance r between the neighboring particles. We are focused on the power-law potentials…
Recently, in the ref. Physica A \bfm{296} 405 (2001), a new one parameter deformation for the exponential function $\exp_{_{\{{\scriptstyle \kappa}\}}}(x)= (\sqrt{1+\kappa^2x^2}+\kappa x)^{1/\kappa}; \exp_{_{\{{\scriptstyle 0}\}}}(x)=\exp…
The effect of the non-extensive form of statistical mechanics proposed by Tsallis on the formation of a quark-gluon plasma (QGP) has been recently investigated in ref. \cite{1}. The results show that for small deviations ($\approx 10%$)…
The kinetic theory of gases provides methods for calculating Lyapunov exponents and other quantities, such as Kolmogorov-Sinai entropies, that characterize the chaotic behavior of hard-ball gases. Here we illustrate the use of these methods…
We demonstrate by simple mathematical considerations that a power-law tailed distribution in the kinetic energy of relativistic particles can be a limiting distribution seen in relativistic heavy ion experiments. We prove that the infinite…
We present a selective overview of the current state of our knowledge (more precisely of ourignorance) regarding the derivation of Fourier's Law, ${\bf J}(\br) =-\kappa {\bf \nabla}T(\br)$; ${\bf J}$ the heat flux, $T$ the temperature and…
This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $\kappa$-distributions) which are frequently observed particularly in high temperature…
We show that the definition of an energy current for non-relativistic systems with action-at-a-distance is possible if the interaction respects Gausses law, i.e. if it is Coulomb-like. The energy current can transport kinetic and mass…
The gas dynamics under external force field is essentially associated with multiple scale nature due to the large variations of density and local Knudsen number. Single scale fluid dynamic equations, such as the Boltzmann and Navier-Stokes…