A generalization of the Thomas–Fermi model within Kaniadakis statistics

While the standard TF model offers computational simplicity, it fails to capture essential quantum and correlation effects, particularly at the nanoscale. To overcome these limitations, we introduce a Kaniadakis-based generalization of the TF model, in which the conventional Fermi–Dirac distribution is replaced by its 𝜅-deformed counterpart. This approach allows for the inclusion of nonextensive and long-range correlation effects while preserving thermodynamic consistency. Analytical and numerical investigations reveal that the 𝜅 parameter introduces two main correction terms in the TF equation.