Power cord supplied with Luxman L-509X Integrated Amp

What is physically happening in the cable that produces a better sound out of the system?

And can it all be measured?

Assuming this was an original US piece, then 2 prongs is all you need, and you'll run into less ground loop / noise problems.

To use 2 prongs the equipment must be double shielded, so that an internal fault won't route the AC's 120V to the chasis.

I still use a shielded power cord however.  This covers the AC wires in a shield that is grounded at the outlet and has no connection at the Luxman for noise reduction.

Most 3 prong cords are not shielded and cheap shielded cords are available on Amazon.

I will start by saying that I rarely use the stock pc’s on any of my gear.
I have a c900u/m900u combo, and several nice pc’s to try from nordost, audioquest, and others.  I found the supplied pc’s were best, just like with Shindo gear.  Tough to say what was different exactly, they just sounded off.  I even asked the importer about this and they also said the included cords are excellent.  He said some liked a aq hurricane on them, which I had tried also. 
Bear in mind that these things are voiced with that cord.  Often a change is perceived as an improvement, when it may not be long term.

I still use a shielded power cord however. This covers the AC wires in a shield that is grounded at the outlet and has no connection at the Luxman for noise reduction. 

Where does the noise come from that gets in there without the shield?
And what is the mechanism that allows it to get in?

Radio. Every wire is an antenna. Do you understand how radio works? Transformers? Same thing.