A simple link of information entropy of quantum and classical systems with Newtonian $r^{-2}$ dependence of Verlinde's entropic force

Abstract

It is shown that the entropic force formula $F_e=-\lambda \partial S/\partial A$ leads to a Newtonian $r^{-2}$ dependence. Here we employ the universal property of the information entropy $S=a+b\ln N$ ($N$ is the number of particles of a quantum system and $A$ is the area containing the system). This property was previously obtained for fermionic systems (atoms, atomic clusters, nuclei and infinite Fermi systems i.e. electron gas, liquid ${}^3$He and nuclear matter) and bosonic ones (correlated boson-atoms in a trap). A similar dependence of the entropic force has been derived very recently by Plastino et al with a Bose or Fermi gas entropy, inspired by Verlinde's conjecture~\cite{Verlide-11} that gravity is an emergent entropic force. Finally, we point out that our simple argument holds for classical systems as well.

8pages, Closely matches the published version in Physica A ( 5 pages, 24 references). Our argument for quantum systems is extended for classical systems as well. Also a slight change has been made accordingly to the title

References in corpus (4)

• Surfaces away from horizons are not thermodynamic
• On the entropic derivation of the $r^{-2}$ Newtonian gravity force
• Quantum treatment of Verlinde's entropic force conjecture
• Spatial cut-offs, Fermion Statistics, and Verlinde's Conjecture

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• The entropic force between two horizons of charged Gauss-Bonnet Black hole in de Sitter Spacetime
• Phase transition and entropic force in Reissner-Nordström-de Sitter spacetime
• Phase transition and entropy force between two horizons in (n+2)-dimensional de Sitter space