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 $\kappa$ (Boltzmann-Gibbs entropy is recovered in the limit $\kappa\to 0$), we show that the scalar and vector meson fields become more intense due to the non-Gaussian statistical effects ($\kappa \neq 0$). From an analytical treatment, an upper bound on $\kappa$ ($\kappa < 1/4$) is found. We also show that as the parameter $\kappa$ increases the nucleon effective mass diminishes and the equation of state becomes stiffer. A possible connection between phase transitions in nuclear matter and the $\kappa$-parameter is largely discussed.