What is the science behind audiophile fuses?

I would posit that fuses are detrimental to audio (from the sound perspective) because they are non linear.  Fuses are designed to be a cascading failure.  The filament heats up as electrical current passes through it.  As it heats up the resistance increases causing further heating.  This filament is delicately balanced to ultimately heat up to the melting point at the rated current.  Besides being a constriction point to the flow of electricity they are also a non linear constriction point.

The ideal fuse would be digital.  That is it would have zero resistance up to the rated current and then go to infinite resistance- a step change.  But the temperature of the filament in a standard fuse is fluctuating with current and therefore the resistance is changing.  So the question is what do audio grade fuses do different?

Does an audio grade fuse act more like an ideal fuse?  Does it have lower resistance or less variation in resistance up to the point of failure at rated current?  Have these audio fuses been tested enough to insure that they will blow at the rated current?

If I had a mega Ohm bridge tester, I would compare the resistance values of a standard fuse side by side with an audio grade fuse at room temp, after cold soaking in a freezer and then after heat soaking in an oven at say, 400F.  That would be interesting data.

If you have to ask about trying an audiophile fuse -

And, depend upon what others say? ...don't bother.

If you can trust your ears?  Then decide.

Well, I have not auditioned or replaced any fuses in any of my systems. I have, however, tried and attest to the positive effects of many of the high-end tweaks out there including some of the products from Synergistic Research. As such, why would well respected companies want to put their reputation on the line if there was nothing to it?

My guess is that there really is something to it, but the explanation is hard to come by. How about trust your ears, we do that with virtually everything else.  

@1extreme Think that's bad? I heard of folks who believe that some invisible deity controls the entire universe. And if you don't talk to it in your mind, you may burn forever. 

...who will look me in the eye and tell me they believe the earth is only 6,000 years old.