Is there a known relationship, either direct or indirect, between physical fitness and musical performance? I haven't been able to find a definitive source or study that confirms my belief that there is a connection between the two, and I'm very interested in knowing if you have. If you have actual, personal experience you could share, that would also help.
This question is open to all musicians, regardless of genre, instrument, or skill level.
I first thought about this question when Garry Kasparov, the chess player, said in an interview many years ago that he exercised as part of his chess training, and swore that this helped his mental abilities required for chess playing. At the time I thought it was silly that something so mental and sedentary as playing chess would benefit from physical exercise. Now that I'm older and wiser, I wonder just how much of what we do as musicians is mental vs. physical.