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arXiv · 1903.08150

Relativistic treatment of Verlinde's emergent force in Tsallis' statistics

L. Calderon·M. T. Martin·A. Plastino·M. C. Rocca·V. Vampa
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Abstract

Following Chakrabarti,Chandrasekhar, and Naina [Physica A {\bf 389} (2010) 1571], we attempt a classical relativistic treatment of Verlinde's emergent entropic force conjecture by appealing to a relativistic Hamiltonian in the context of Tsalli's statistics. The ensuing partition function becomes the classical one for small velocities. We show that Tsallis' relativistic (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 Renyi's distribution, the attempt fails and one needs to modify the conjecture.

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L. Calderon, M. T. Martin, A. Plastino, M. C. Rocca, V. Vampa. 2019-03-19. Relativistic treatment of Verlinde's emergent force in Tsallis' statistics. https://doi.org/10.1142/s0217732319500755

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