Quantum statistical treatment of Verlinde's conjecture in a Tsallis framework

M. C. ROCCA; A. PLASTINO

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2019 vol. 517 p. 1 - 7

0378-4371

Verlinde has recently conjectured, via a Beckenstein-like thought experiment, that gravitation, instead of being an elementary force, is an emergent entropic one.This rather surprising conjecture was actually proved in [Physica A {f 505} (2018) 190], in astrictly classical statistical mechanics´ environment. In this Communication, we work in a quantum statistical context to considerthe conjecture in the case of bosons/fermions, in a Tsallis´ framework. We prove that Tsallis´ entropy is the operating potential energy in this quantum treatment, something that does not happen in the case of Boltzmann-Gibbs´ entropy. In the classical limit, we show that the emergent force has a Newtonian dependence with the distance