I've done fasts on relatively nothing for over five days. Early on, you get some "empty-stomach intelligence" where your mind is just more alert because of plenty of oxygen (from not digesting) and probably some evolution that favored apes that got observant and driven when hungry as opposed to lazy.
Fasting long enough to get the effects in the paper will use up all your glycogen stocks. Read wiki on starvation for details, but basically you want to have a small supply of starches to keep your skeletal muscle from breaking down to feed your brain. About two days in, without some glucose supply, you will unavoidably slow down. Lethargy will commence when your brain is starving. It is not euphoric. It is the world slipping out of grip without you noticing.
As long as your taking care of your mandatory glucose supply, fasting over three days or more will lead to a common theme in all nutrition and health papers: all processes that break things down for re-use are up-regulated and all processes that consume resources are down-regulated.
It's not difficult to propose that a system composed of mostly brand-new, turned over cells and muscles with all their proteins aligned to the principle stresses is more protein efficient than one resulting from plenty of nutrients floating around like entrepreneurs with too much money. Fasting would be expected to result in general house-cleaning so that protein that's not accomplishing much ends up reallocated to doing something useful.
Some examples of where this shows up in scientific papers is the increased sensitivity to chemotherapy of cancer cells when the patient is fasting. One proposed mechanism was an up-regulation of registration for immune-system induced self-destruction through the normal pathway; a badly functioning protein might go ahead and function sufficiently in the up-regulated pathway.
More obvious benefits from fasting are the same as those of anything where you build up self-discipline and also getting in touch with the difference between hunger and a lack of being full; they are much more distinct after a fast. Cravings for sugar are gone because your hormones for hunger and satiety are all operating properly, as is your pancreas.
My favorite way to get empty is to just drink water and/or coffee (black) or tea. Fluids, no macro-nutrients. Get some glucose from some bread. Get some micro-nutrients from some yogurt and rabbit food. Let the rest slip into the starvation mode. Stress level and blood pressure will decline into a kind of euphoria as long as you don't over-do the calorie starving to the point that you're thinking on muscle protein.
I've done it. All the mechanisms have obvious symptoms. If you are just ketogenic and in starvation, you feel euphoric and completely without variations in energy. If you are beyond starvation and skeletal protein is being converted to glucose, you piss dark yellow and feel like you're on anesthetic. Either way you lose a lot of weight, your energy will regulate much more tightly, and you won't be bothered by hunger, and you'll be drinking coffee as nature intended it instead of some holiday special milk-shake.
It's well-established that reduced calorie diets promote longevity and that the spectrum of metabolic syndrome conditions are associated with all sorts of bad things, so although I'm not a doctor, I don't expect to have any regret about recommending anyone try coffee fasting to put their system through its paces.