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 reinterpreted: 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.

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