connective derivations

There are multiple derivations associated with waveguides. However, I don't see derivations focused on waveguides as being connective to any other topic.

Similarly the Navier-Stokes equation for fluids doesn't seem to relate any topics (though I have less experience with this compared to waveguides).

• There is probably a "connective derivation" that relates Quantum Mechanics to Statistical mechanics, probably involving the definition of entropy. 
• Another connection is that Statistical mechanics is related to thermodynamics (again, not clear what derivation would show this). 
• classical mechanics and astrophysics are based on the same concepts
• There should be a relation between (classical motion) and (relativity) since the difference is the assumptions about slow versus fast objects.
• Wave-particle duality present in optics relates to atomic theory
• the orbit of Mercury relates astrophysics to relativity
• thermodynamics connects to quantum mechanics in the black-body radiation experiment
• quantum field theory relates relativity to quantum

I don't have insight on how electrodynamics relates to quantum mechanics or how electrodynamics relates to classical mechanics.