Sure the body is, like everything else, a heat engine.
It seems we all agree upon this principle, but when it comes to its application opinions differ.
...we don't have a good way of comparing the available energy from those different fuels, and the body uses them in very different ways.
No argument here either.
To say a "calorie" from fat will cause the same about of fat gain as a "calorie" from carb or from prtoein assumes that the body extracts the same amount of energy from each type of food that a bomb calorimiter does, and that the body will use each nutrient in the same way and obtain the same amount of energy from each.
Again, if the "calorie" in this sentence stands for "as measured by a calorimeter and appears in the tables as the caloric value of certain foods" there is no argument. People do differ as of the digestion effectiveness and utilization percentage, and even for the same person these may change according the factors like hormonal state etc. (Hurray to Cortisol(*)). However, these tables are not that far from the truth, and healthy people do tend to have close values, otherwise all those RMR/BMR calculations were not of any value, while in fact they tend to be close to the truth for most people. The standard error the FAO gives for its BMR calculation is about 100 calories for females (see table 5.2 in http://www.fao.org/docrep/007/y5686e/y5 ... #TopOfPage
), so, like in so many other areas, we're not as unique as we'd like to think ("You are unique, like everyone else" :-)). Your very own profession is based on this fortunate fact, until we get to the promised land of individual medicine, that is. And, most importantly, we do know the only possible direction of the error for those people who are at the tail of the distribution function.
Keeping activity constant, consuming a certain number of fat calories will not give the same results as the same number of carb calories. Just doesn't happen that way in real life, no matter how one's understand of thermodynamics may argue otherwise. No, you can't violate the laws of thermodynamics, but we just don't understand all we need to as to how they apply to the human body.
But we do understand them well enough to know you can't break them as you yourself said. We do understand them well enough to know they set limits that are not affected by the inner workings of the machine we call the human body, and we do know no amount of Cortisol on this planet will let you extract 1500 calories of a thousand calory consumption (I may extract 950, you may extract 980, none of us will extract 1001). This, again, is agreed upon by all of us at least at the level of paying lip service to the principle, up to the point of me being accused that by raising this trivial point time after time I'm arguing with a strawman, but when it comes to a trainee who claims to be in a steady state
on 1000 calories a day while exercising for almost 2 hours daily- at least 4 or 5 standard errors off the charts (in the wrong
direction. i.e. not wasting eaten calories by turning them to heat which is possible, but rather utilizing more energy than the calorimeter says there are when the food is totally burned), people still argue for the feasibility of this situation. Kpj seems like a serious fellow, willing to learn and improve, and I have nothing but respect for him. I could only wish to have instructors like him, and that's the reason I think treating his misconceptions under the "we don't know enough" umbrella is doing him, and his clients, disservice. His clients are doing something wrong, either lying to themselves or to him, and he can be a better trainer if he realizes it (I have no idea what he should do with the knowledge, but he should know. For the least he should keep in his mind this might be a case of eating disorder, which might eventually call for medical intervention). The same is true for millions of people all over the world who claim to be gaining weight while eating less than their calculated DMR (D = Daily). Sure, there are few who really have a slow metabolism (the thyroid gland being a main suspect, as you doctors know so very well), but it shows in their activity level and it can never fall under the BMR, which is the minimum energy needed to sustain life.
Sorry, this has turned out to be longer than intended, and mostly a repeat of stuff I have already said. My only saving grace is that people are not reading long posts anyway.
(*) BTW, if chronic high level of Cortisol is bad, and if starvation raises this level, how do modern medicine explain the phenomenon of increased life span through caloric deficiency diet?