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arXiv · 1812.07984

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

A. Plastino·M. C. Rocca
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Abstract

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 {\bf 505} (2018) 190], in a strictly classical statistical mechanics' environment. In this Communication, we work in a quantum statistical context to consider the 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. \color{red} In the classical limit, we show that the emergent force has a Newtonian dependence with the distance.

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A. Plastino, M. C. Rocca. 2018-11-22. Quantum statistical treatment of Verlinde's conjecture in a Tsallis framework. https://doi.org/10.1016/j.physa.2018.10.056

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