Cosmological considerations in Kaniadakis statistics

We have shown that the connection between the number of bits and the area of the holographic screen, where both were established in Verlinde's theory of entropic gravity, may depend on the previously chosen thermostatistics theory. Starting from the Boltzmann-Gibbs (BG) theory, we have reobtained the usual dependence of the number of bits and the holographic screen area. After that, using the Kaniadakis microcanonical entropy formula within the entropic gravity formalism, we have derived another relation between the bits number and the holographic screen area. We have used this new relation to derive three Newtonian-type accelerations in the context of Kaniadakis' statistics which are a modified gravitational acceleration, a modified MOND theory and a modified Friedmann equation. We have obtained a kappa version of the Tully-Fisher (TF) relation which displays a dependence of the distance from the star in contrast to the standard TF expression.