Non-gaussian statistics and the relativistic nuclear equation of state

Abstract

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 $κ\to 0$), we show that the scalar and vector meson fields become more intense due to the non-Gaussian statistical effects ($κ\neq 0$). From an 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.

8 pages, 8 fifures, LaTeX