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 → 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.

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