If you boil food in water, does the volume of water matter for the amount of flavorful compounds lost to the water?

I'm going to take my life in my hands here and hypothesize that the answer is "It all depends", assuming of course that everything is identical, apart from the volume of the water.

The first challenge is how are you going to objectively determine loss of flavour? If you were to subject the "Sample" and the "Water" to mass spectrometry for instance, you quite possibly could detect a discernable difference between experiments, especially if your food sample was very large and the water volume very small. For instance, certain salts would transfer from the food into the water, and once saturation point is reached, the water would not be able to absorb any more. Would reaching that equilibrium prevent a further deterioration of flavour? Quite possibly so, if salt was a major constituent of flavour for that particular food sample.

On the other hand, if the food sample was very small and the water volume was very large, salt would easily be expelled (unrestricted by saturation) to the point that the food no longer chemically resembled the original. Ergo, your sample would have suffered from loss of flavour. This conceivably could be offset by reabsorption, so it might not be total.

We haven't even started to examine in depth the chemical composition of the sample, any effect that a specific environment may have e.g. evaporation, pressure, Brownian motion, or just simply the heating methods used (radiant heat, microwave, pressure cooker, open pan, closed pan etc.). These may affect the speed of the process, the physical deterioration of texture etc. Nor have we covered different foodstuffs, a complex bony piece of meat or cartilage will respond differently to a more simple piece of vegetative matter. Using a piece of iceberg lettuce for instance, would probably give the answer "No" under both scenarios, as it would be difficult to find any situation where an observer could truthfully state that it actually tastes of anything.

Taking a step back from the realms of chemistry, physics etc, within normal limits (e.g. same food size, same temperature and cooking time, different water volume), it would be difficult for a individual to objectively "Taste test" the difference between the two scenarios. Eventually, both scenarios end up with a tasteless mush or the food dissolving completely. I'm not saying there wouldn't be any losses at the molecular or sub-atomic level, as boiling, pressure cooking and steaming food clearly result in very different outcomes when it comes to taste, aroma and texture. Which just goes to demonstrate the major effect even a slightly different scenario has on the whole shebang.

Probably the best definitive example would be cooking a brined fish. Large water volume, and probably all the salt (and therefore a core constituent of flavour) would eventually pass into solution. A small volume with a very large fish would rapidly cause saturation of the water to be reached and the fish would in theory, retain some taste. On the other hand, a raw carrot would probably, like the lettuce, demonstrate complete and total indifference.