Searching for the appropriate noun, I wonder why Duden knows Asymmetrie, but not Unsymmetrie - is the latter plainly wrong?
I don't think this is so much a German question as a math question. In English, the word "asymmetrical" is a special kind of symmetry where the polarity changes when you flip it about the axis. "Unsymmetrical" would simply indicate a lack of symmetry altogether.
Here is an example that shows how these concepts are applied in quantum mechanics. We want to write the wave function of an electron concentrated in the left side of a double well. We can write this as the sum of the symmetrical case plus the antisymmetric case. When we add the two togther, the portions in the right hand well cancel out and the wave is found all on the left hand side. That is an unsymmetrical (or non-symmetrical) situation.
We do this in physics because the symmetrical and the asymmetrical cases have especially simple mathematical descriptions. So the non-symmetrical case is most easily analyzed as the sum of the two special cases. This particular problem occurs when we ask the question: how long does it take for an electron in the left hand side to move entirely to the right hand side (a typical "tunneling" question).