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Boltzmann entropy-based thermodynamics of charged anti-de Sitter (AdS) blackholes has been shown to exhibit physically interesting features, such as $P-V$criticalities and van der Waals-like phase transitions. In this work we extendthe study of these critical phenomena to Kaniadakis theory, which is anon-extensive generalization of the classical statistical mechanicsincorporating relativity. By applying the typical framework of condensed-matterphysics, we analyze the impact of Kaniadakis entropy onto the equation ofstate, the Gibbs free energy and the critical exponents of AdS black holes inthe extended phase space. Additionally, we investigate the underlyingmicro-structure of black holes in Ruppeiner geometry, which reveals appreciabledeviations of the nature of the particle interactions from the standardbehavior. Our analysis opens up new perspectives on the understanding of blackhole thermodynamics in a relativistic statistical framework, highlighting therole of non-extensive corrections in the AdS black holes/van der Waals fluidsdual picture.

$P-v$ criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics