What is a minimal step angle deflection for flight control surfaces?
There are several phenomena that may affect the asked resolution. The easier one is the static (steady case), and the dynamic case which requires several more analyses. 

Statically, the resolution of any surface will determine the moments that that particular surface can generate. Consider the elevator, the resolution will determine which aoa and which speeds the aircraft will be able to fly (with a given weight and a given thrust configuration). 

Dynamically, the stability of the plane will derive the required resolution. Consider the elevator, and suppose your resolution is 1 degrees. The inputs will generate short period and long period (phugoid) modes simultaneously and your controller will become a bang-bang controller, because you can only command increments (decrements) of 1.

Hope these give some clues to understand the physics. For more details, control theory will be useful.