  Employing a thermodynamic interpretation of gravity based on the holographic
principle and assuming underlying particle statistics, fermionic or bosonic,
for the excitations of the holographic screen leads to Modified Newtonian
Dynamics (MOND). A connection between the acceleration scale $a_0$ appearing in
MOND and the Fermi energy of the holographic fermionic degrees of freedom is
obtained. In this formulation the physics of MOND results from the
quantum-classical crossover in the fermionic specific heat. However, due to the
dimensionality of the screen, the formalism is general and applies to two
dimensional bosonic excitations as well. It is shown that replacing the
assumption of the equipartition of energy on the holographic screen by a
standard quantum-statistical-mechanics description wherein some of the degrees
of freedom are frozen out at low temperatures is the physical basis for the
MOND interpolating function ${\tilde \mu}$. The interpolating function ${\tilde
\mu}$ is calculated within the statistical mechanical formalism and compared to
the leading phenomenological interpolating functions, most commonly used. Based
on the statistical mechanical view of MOND, its cosmological implications are
re-interpreted: the connection between $a_0$ and the Hubble constant is
described as a quantum uncertainty relation; and the relationship between $a_0$
and the cosmological constant is better understood physically.
