Non-Gaussian statistics and the relativistic nuclear equation of state

We investigate possible effects of quantum power-law statistical mechanics on the relativistic nuclear equation of state in the context of the Walecka quantum hadrodynamics theory. By considering the Kaniadakis non-Gaussian statistics, characterized by the index κ (Boltzmann–Gibbs entropy is recovered in the limit κ→0), we show that the scalar and vector meson fields become more intense due to the non-Gaussian statistical effects (κ≠0). From a analytical treatment, an upper bound on κ (κ<1/4) is found. We also show that as the parameter κ increases the nucleon effective mass diminishes and the equation of state becomes stiffer. A possible connection between phase transitions in nuclear matter and the κ-parameter is largely discussed.