On the entropic derivation of the $r^{-2}$ Newtonian gravity force

Abstract

Following Verlinde's conjecture, we show that Tsallis' classical free particle distribution at temperature $T$ can generate Newton's gravitational force's $r^{-2}$ {\it distance's dependence}. If we want to repeat the concomitant argument by appealing to either Boltzmann-Gibbs' or Renyi's distributions, the attempt fails and one needs to modify the conjecture. Keywords: Tsallis', Boltzmann-Gibbs', and Renyi's distributions, classical partition function, entropic force.

10 pages. No figures

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• Phase transitions and entropy force of charged de Sitter black holes with cloud of string and quintessence
• Tsallis' entropy, modified Newtonian accelerations and the Tully-Fisher relation
• Relativistic treatment of Verlinde's emergent force in Tsallis' statistics
• Newton's gravitation-force's classical average proof of a Verlinde's conjecture
• Spatial cut-offs, Fermion Statistics, and Verlinde's Conjecture
• Quantum statistical treatment of Verlinde's conjecture in a Tsallis framework
• Realize Emergent Gravity to Generic Situations
• Depletion force between disordered linear macromolecules