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.
