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.

💡 Research Summary

The paper explores how a non‑Gaussian statistical framework, specifically the Kaniadakis κ‑statistics, modifies the relativistic nuclear equation of state (EOS) derived from the Walecka quantum hadrodynamics (QHD) model. In the conventional treatment, nucleons are described by a Fermi‑Dirac distribution based on Boltzmann‑Gibbs (BG) entropy, and the scalar (σ) and vector (ω) meson fields are obtained from self‑consistent mean‑field equations. The authors replace the BG distribution with the κ‑exponential form
( n_{\kappa}(p)=\big