Another trivial example of non-superposition. This one is for a scaler
field. The temperature in a cabin is the same as outdoor, -10 degr. You
turn an electic heater on and wait till a new equilibrium temerature,
+5 degrees, is established. Do the same with a more-power heater and the
new temp. is +20 degrees. In the first case dT was 15 in the second
it was 30. Run both heaters at the same time. You know that the third
dT will be less than 15+30=45. Why? Because the rate of loosing heat
increases with dT (Newton's law of cooling).
Ludwik Kowalski
P.S.
In the same spirit the final result of using two vacuum pumps (a change
of air pressure in a leaky vessel) is not the sum of what can be done
with each pump. You will have a lower pressure while using two pumps
simultaneously but not as low as it would be if the principle of
supperposition was applicable. I agree that it is not necessary to go to
quantum chromodynamics (quarks and gluons) to find cases of non-additivity.