No, there is no technical reason why a heavier gauge power cord would provide any benefit whatsoever.
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While there may be no technical reason a larger guage cord will work better, my experience is that the larger guage cords that I have tried have been better performers overall with my integrated amplifier. I have not tried anything heavier than 10 guage but I think that a heavier cord may have advantages over a smaller one with a fairly current hungry piece of equipment. With my digital gear, I have not found that guage is as significant, and actually use a 26 guage DIY cord on my DVD player that sounds better than a Cardas Golden cord which I had used on that piece before. I wouldn't consider, however, even putting that cord on my amp for obvious reasons.
I have replaced all of my stock powercords with DIY cords via Chris VenHaus recipes. I did the first one because the dollar investment was minimal and if it didn't work that well I would not be out very much. I replaced all of the cords because the sonic differences were not subtle, but huge.
It is possible to buy astronomically expensive cords, which I have never done so I cannot address the value of them, but great improvements can be had for under $100 if you don't mind doing a little work.
I don't know if just adding heavier gauge cable will do much for you, you need the right cable. I used Beldon 83802 for all of my cables.
Try a better cord, you won't go back to stock cords again!
I believe it is mostly folklore that heavier gauge cables are a must.
But I do believe that heavier gauge cables can potentially help compensate for possible design flaws, inefficiencies, and/or simply added for increased marketing hype.
And of course the garden hose thickness always gives the consumer the impression they are getting their monies worth. There's that WoW! factor there that is impressive every time my mother-in-law saw my old thick cables.
I know you are asking about power cables. But if you look at say the Audience Au24, Audio Tekne, or Nordost Valhalla speaker cables, you will notice that these cables buck the traditional heavy gauge speaker cable trend that we have been told must be present for proper sonics.
The Audience Au24 speaker cables are no thicker than my keyboard cable connected to my computer. And the Au24's are the best I've heard, especially in the bass and mid-bass regions. Simply an awesome cable at a reasonable price.
I believe the same holds true for power cables. To a point anyway, heavier gauge simply helps convince the buyer that they are buying a product of substance(even if they are not).
Please don't get me wrong though. I'm sure there are plenty of excellent power cables mfg'ered with heavy gauge cabling. I just don't think it's an absolute necessity as some would have us believe.
I dont know how to explain this, but i think some larger cables perform better than some small ones and vice versa.My current system sounds best with heavier guage cables,but my last sounded better with thinner cables including the power cords.I know most inwall wires are 14Guage,so why would I use 10awg power cords from a 14awg wall receptical?The same reason why most heavy duty power tools use heavy guage power cords,also the same reason why many audiophiles run 10awg speaker cable to speakers who's internal wireing is between 14-16awg.The same goes for heavy guage interconnects that will plug into a component who's internal wireing is only 18-20awg.All I know is well designed heavy guage cables are excellent in the right system,no matter how thin the inwall wire is.
I don't go out of my way to buy heavier power cords, per se. I did buy an eight foot granite audio power cord a while back for the simple reason that I did not want to use an extension cord. I use it on my CD player and I do believe I can hear a differance. As I have over the years collected a surplus of power cords, I do use the heavier gauge cords and and I store the lighter ones in a box. Again, keeping in mind that your question was simply one of heaver gauge cords. You did not ask about all of the specialized high-end cords available.
One interesting thing you can do is replace the cheap two wire cords that come with many DVD and Cd players with a used computer cord that has some shielding which is available at any used computer store. It can't hurt, and it might make you feel better.
Heavier gauge cables typically have a greater amount of dielectric around each conductor. As such, this can change the impedance of the cable as a whole. Dielectric absorption may also become a bigger factor as you have more surface area of the larger conductor that comes into contact with a larger area of insulating material.
Other than that, heavier gauge cables keep series resistance to a minimum and thermal losses are minimized. Sean