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A simple link of information entropy of quantum systems with Newtonian r − 2 dependence of Verlinde’s entropic force

2018; Elsevier BV; Volume: 518; Linguagem: Inglês

10.1016/j.physa.2018.12.018

1873-2119

C. P. Panos, Ch. C. Moustakidis,

Statistical Mechanics and Entropy

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.