  Entropic force has been drawing the attention of theoretical physicists
following E. Verlinde's work in 2011 to derive Newton's second law and
Einstein's field equations of general relativity. In this paper, we extend the
idea of entropic force to the distribution of quantum particles. Starting from
the definition of Shannon entropy for continuous variables, here we have
derived quantum osmotic pressure as well as the consequent entropic forces for
bosonic and fermionic particles. The entropic force is computed explicitly for
a pair of bosons and fermions. The low temperature limit of this result show
that the entropic force for bosons is similar to Hooke's law of elasticity
revealing the importance of this idea in the formation of a Bose-Einstein
condensate. For fermions, the low temperature limit boils down to the well
known Neumann's radial force and also reveals the Pauli's exclusion principle.
The classical limit of the entropic force between quantum particles is then
discussed. As a further example, the entropic force for quantum particles in
noncommutative space is also computed. The result reveals a violation of the
Pauli exclusion principle for fermions in noncommutative space.
