We propose to put the well-known nonthermal and suprathermal empirical distributions, used in plasma physics, onto a more rigorous foundation. Their use is frequently criticized because of a lack of formal derivation and physical explanation. A connection between these non-Maxwellian distributions and the Beck-Cohen superstatistics is suggested. They are perceived as a consequence of typical temperature fluctuations. We show that the suprathermal distribution is generated by the $$\Gamma${}$ distribution of the inverse temperature, in the same way as the Tsallis $q$ statistics. The nonthermal distribution also follows from the ${$\chi${}}^{2}$ distribution, with a small variance. Our contribution provides a possible physical meaning for these ad hoc distributions.

Blackbody radiation is reconsidered using the counterpart of the Bose-Einstein distribution in the $$\kappa${}$ statistics arising from the Kaniadakis entropy. The generalized Planck radiation law is presented and compared to the usual law, to which it reduces in the limiting case $$\kappa${}$\rightarrow${}0$. Effective Einstein's coefficients of emission and absorption are defined in terms of the Kaniadakis parameter $$\kappa${}$. It is shown that the Kaniadakis statistics keeps unchanged the first Einstein coefficient $A$ while the second coefficient $B$ admits a generalized form within the present theoretical framework.

Because of the long-range nature of the gravitational interaction, self-gravitating systems never reach thermal equilibrium in the thermodynamic limit but remain trapped in nonequilibrium stationary states, or quasiequilibrium states. Here, we deal with quasiequilibrium self-gravitating systems by representing them as a collection of smaller subsystems that remain infinitely close to equilibrium. These subsystems represent regions from where thermalization spreads later over the whole system. Such a methodological attitude allows representing their statistical properties as a superposition of statistics, i.e., superstatistics. It has the advantage of producing Tsallis distributions, widely used in fitting observational data, as a special case of a more general family of distributions, while relying only on conventional statistical mechanics. Focusing on the three universality classes of superstatistics, namely, ${\chi }^2$, inverse-${\chi }^2$, and log-normal superstatistics, we discuss the velocity distributions arising in this picture and confront them with independent numerical simulations. Then, we study the consequences on typical phenomena arising in self-gravitating systems. We discuss the Jeans instability in the classical regime, for a static and an expanding universe, and extend our results to the quantum regime by applying the Wigner-Moyal procedure. Our results reveal that quasiequilibrium systems remain stable for larger perturbations, as compared to equilibrium systems, meaning that a larger mass is needed to initiate the gravitational collapse. This is particularly relevant for Bok globules because their mass is of the same order as their Jeans mass; hence, a small deviation from equilibrium may lead to a different prediction for their stability. We also discuss the Chandrasekhar dynamical friction in a quasiequilibrium medium and analyze the consequences on the decay of globular orbits. Our results suggest that the superstatistical picture may offer a partial solution to the problem of the large timescales shown by numerical $N$-body simulations and semianalytical models.

Quantum ion-acoustic solitary waves are studied by considering the effects of exchange and correlation for the electrons. Starting from one-dimensional quantum hydrodynamic equations, including the term of exchange correlation for electrons, we obtain a model in which two dimensionless parameters appear (in addition to the parameter measuring the quantum diffraction) measuring the exchange and the correlation. A new deformed Korteweg–de Vries equation is derived. The effect of exchange and correlation is reflected in the phase speed as well as in the nonlinear and dispersion terms. Its solution shows that the exchange-correlation effects modify the amplitude as well as the width of the weak solitary waves. In the arbitrary amplitude regime, and as may be expected, a pseudopotential analysis shows that the exchange-correlation effects may change the nature (compressive or rarefactive) of the quantum ion-acoustic solitary waves. Our results complement and give new insight into the previously published work on this problem.