Nutrition and Conservation of Energy

Further to my previous post, I am working out how energy balance (calories in vs. calories out) relates to changes in body weight.
To explain where I am coming from: both energy balance and mass balance provide (different) holistic views of the human body as a system – with biochemistry and physiology providing the ‘zoom-in’ detail.
What I am trying to do is meld them all into a consistent mental model – at least for myself.
I still find the conservation of mass view easier to understand conceptually, but mostly I think because of the short cuts taken in describing the conservation of energy view. The latter is certainly a much more common approach.

 
Conservation of energy does, of course, apply to the human body. Energy into the body must match energy out: E(stored) = E(in) - E(out), this is a fundamental law of physics. The problem is how this relates to body mass - and especially body fat - since mass and energy are not interchangable in chemical reactions.
There is an implicit step in most discussions that is not called out - mostly I think since the majority of people don't care. This is the mapping of variables to aspects of nutrition. Hence:
* E(in) = energy consumed in food. This mapping seems self-evident - which, to a scientist, means it needs to be treated with suspicion. I can understand that there is little energy extractable directly from liquid or gas and so solid input can be considered the only source. Although dissolved solid such as sugar in water also need to be considered.
* E(stored) = fat, sort of. This is useful as a first approximation since other storage mechanisms, such as glycogen and tissues such as muscle have limited energy capacity - and are usually full. It is also the point where energy and mass are most confused. Chemical potential energy is stored in fat in the same way a battery stores energy. Or, since fat is created or destroyed as needed, more like water in a dam supplies hydro-electricity. The water is not energy but the water level can be used to estimate how much energy is being held
* E(out) = energy expended. This is the point where I have most trouble. There are multiple points where energy leaves the body and burning (oxidising) fat is only one of them. BUT, there is no weight loss at the time! The weight is not lost until the by-products of burning the fuel leave the body - things such as carbon dioxide or uric acid and other waste products. There is also energy which was never claimed by the body which escapes in solid form - food residues that were not fully digested

I think it is in the middle there that the talk about calories loses its traction. Weight loss is related to loss of substance, of material, from a body. Burning fat to release energy might be the underlying reason why waste products need to be removed but it is the actual removal of the "ash" that results in weight loss.
Most of the articles I have seen talk about the different ways in which energy is expended without ever discussing this final step in the process.

For a number of reason I still find conservation of mass a better way of thinking about the issue.
For instance - the way that waste products are removed nearly always requires water and so, while restricting fluid intake reduces weight in the short term, it is a very BAD approach for health - or long term results.
(BTW - thanks to Peter Attia for letting me work some of this out in his blog comments)