The human brain is a large energy consumer, just like data centres use up much electricity.
Fischer used to hold his breath under water in a swimming pool. He believed that would enable his body to supply more oxygen to his brain while playing chess.
Knowing the right "chunks" is so much more important than being physically fit. Although you shouldn't be in such a bad state that you blunder, so you should have slept well and haven't had too much stress before.
But there's hardly any difference between a physically fit player and a couch potato in terms of chess on amateur level. It is grossly overrated in my opinion.
PS: Fitness gives you other types of fun in life, amongst my other hobbies are mountainbiking and swimming. But comparing my chess results I found only spurious correlations.
It depends on what kind of time control you play. I think if you play a few blitz games or so it's not very relevant, however if you play a tournament with two 5 hour games per day you will DEFINITELY profit from a good endurance especially in the second half of the tournament where you can really see the not so fit players blunder left and right.
Brain needs oxygen and energy (glucose) to work correctly. Any physical activity may improve this ability.
Heart rate increase during an OTB game (oh no, am i the only one having this problem ?!) and 90-110 bpm (even more ?) is similar to endurance sport.
I think sport cannot give you the win. But hydratation, nutrition, sleep, no smoking, well-being are factors that increase the probabilty to win
I twice won my club's blitz championship (defeating the local FIDE Master) after a day long of garden labor and despite being physically tired. It seemed as if I could think clearer and faster than usual.
I played well in a strong open, and held a draw with black in a rook ending against an international master after 3 weeks of 7.5 km cycling races against my brother.
I earned my first FIDE rating (at that time it was only awarded above 2200) in an international open tournament where I swam in the sea every morning.
It may be a coincidence, but I certainly had no more or less chuncks of knowledge in those events than in other ones.
Especially in tournaments with classical time control, stamina is important. Many games are lost by blunders in the 4th hour that may be attributed to physical factors, not to knowledge.
