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I don't refuel for the next run as I'm trying to lose weight. Running acts as a good appetite suppressant, I can go out for the run feeling quite hungry and when I'm back I don't feel hungry at all (and not for a good few hours afterwards). I'm aiming to run a 3500kcal/week deficit to give me 0.5kg/week weight loss so I need all the help I can get.
Depending on what you're training for, there is the theory of (on occasion) "running on empty", as a way to teach your body to burn a higher proportion of fat.
It certainly works. When I first got into Audax I'd be ravenous at the first control (50km or so). After a while I'd do my usual DIY ride up to Cambridge and back starting on an empty stomach and having my first food at the half way mark (~110km). After lots of riding I could do the entire thing without resorting to any food (I'd carry some in case I ever got close to bonking). It's useful as the first proper control on PBP is at ~220km although most people stop at a cafe along the way (Cafe des Sports in ??? is a classic) or get something at the optional control at ~140km.
Depending on what you're training for, there is the theory of (on occasion) "running on empty", as a way to teach your body to burn a higher proportion of fat. For marathon training I'm usually quite happy doing a pre-brekky 20+ miles in the morning, on a coffee and a pint of water. If it's cool weather I might get round without any drinks, although even in Winter it's useful to know where the water fountains are. Summer training for an Autumn marathon will involve knowing where the water fountains are, plus planning a drink stop at a shop maybe half way round, preferably something sugary and isotonic. Only really take gels when I'm trying something out pre-race, just to make sure it agrees with me.
For most runs up to 15 miles or so I'll just make sure I refuel and hydrate really well after the run.