I have heard repeatedly the argument about "calories in, calories out" (e.g. here). Seems to me that there are a few unspoken assumptions, and I would like to ask how true they are in reality. Here are the assumptions:

a) all calories in the food you put in your mouth are digested;

b) the digested calories are either stored as fat or spent as work; there is nothing else that could happen with them;

and in some more strawmanish forms of the argument:

c) the calories are the whole story about nutrition and metabolism, and all calories are fungible.

If we assume these things to be true, it seems like a law of physics that if you count the calories in the food you put in your mouth, and subtract the amount of exercise you do, the result exactly determines whether you gain or lose fat. Taken literally, if a healthy and thin person starts eating an extra apple a day, or starts taking a somewhat shorter walk to their work, without changing anything else, they will inevitably get fat. On the other hand, any fat person can become thin if they just start eating less and/or exercising more. If you doubt this, you doubt the very laws of physics.

It's easy to see how (c) is wrong: there are other important facts about food besides calories, for example vitamins and minerals. When a person has food containing less than optimal amount of vitamins or minerals per calorie, they don't have a choice between being fat or thin, but between being fat or sick. (Or alternatively, changing the composition of their diet, not just the amount.)

Okay, some proponents of "calories in, calories out" may now say that this is obvious, and that they obviously meant the advice to apply to a healthy diet. However, what if the problem is not with the diet per se, but with a way the individual body processes the food? For example, what if the food contains enough vitamins and minerals per calorie, but the body somehow extracts those vitamins and minerals inefficiently, so it reacts even to the optimal diet as if it was junk food? Could it be that some people are forced to eat large amounts of food just to extract the right amount of vitamins and minerals, and any attempt to eat less will lead to symptoms of malnutrition?

Ignoring the (c), we get a weaker variant of "calories in, calories out", which is, approximately -- maybe you cannot always get thin by eating less calories than you spend working; but if you eat more calories than you spend working, you will inevitably get fat.

But it is possible that some of the "calories in (the mouth)" may pass through the digestive system undigested and later excreted? Could people differ in this aspect, perhaps because of their gut flora?

Also, what if some people burn the stored fat in ways we would not intuitively recognize as work? For example, what if some people simply dress less warmly, and spend more calories heating up their bodies? Are there other such non-work ways of spending calories?

In other words, I don't doubt that the "calories in, calories out" model works perfectly for a spherical cow in a vacuum, but I am curious about how much such approximation applies to the real cases.

But even for the spherical cow in a vacuum, this model predicts that any constant lifestyle, unless perfectly balanced, should either lead to unlimited weight gain (if "calories in" exceed "calories out") or unlimited weight loss (in the opposite case). While reality seems to suggest that most people, both thin and fat, keep their weight stable around some specific value. The weight itself has an impact on how much calories people spend simply moving their own bodies, but I doubt that this is sufficient to balance the whole equation.