  In this letter, we present the unified paradigm on entropy-ruled Einstein
diffusion-mobility relation ({\mu}/D ratio) for all dimensional systems (1D, 2D
and 3D) of molecules and materials. The different dimension-associated
fractional value of the variation in differential entropy with respect to the
chemical potential ({\Delta}h/{\Delta}{\eta}) gives the quantum-classical
transition version of {\mu}/D relation. This is a new alternative version for
quantum devices, instead of Einstein original relation of {\mu}/D = q/kT; where
q, k and T are the electric charge, Boltzmann constant and temperature,
respectively. It is found that the fractional value of {\Delta}h/{\Delta}{\eta}
for {\mu}/D ratio for different dimensional systems or devices is a direct
consequences with the average energy-Fermi energy relation, which can varies
with the typical dimensions, whether the system belongs to 1D or 2D or 3D. This
unified entropy-ruled transport formalism works well for both the quantum and
classical systems with equilibrium as well as non-equilibrium conditions. Based
on the dimensional dependent entropy-ruled {\mu}/D factor, the
Navamani-Shockley diode equation is transformed.
