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The 1st Law of Thermodynamics Says Energy Stored Equals "Calories In" Minus "Calories Out"
The 1st law of thermodynamics is the source of our two main hypotheses about what makes us fat: Caloric Balance and Lipophilia.
According to Caloric Balance, the quantity of calories we eat matters.
According to Lipophilia, the quality of the calories we eat matters. (In particular, it's how the calories we eat impact fat tissue metabolism.)
So what does the evidence say? Are all calories equal or not?
Here's one article that seems to support Lipophilia. It's from the Journal of Nutrition. To quote from the abstract:
"A widely held belief in both the popular and technical literature--that "a calorie is a calorie"--is analyzed and found to be without foundation on purely thermodynamic grounds. More precisely, the content of the belief--that, for given purposes (e.g. losing weight), it does not matter where your calories come from as along as they amount to the same magnitude (i.e. technically, an isocaloric diet)--is shown to be authorized only by the first law of thermodynamics and not by the second law of thermodynamics.[1]
You can read more about the arguments against the idea that a calorie is a calorie here and here.
So this sets up our first battleground. Which hypothesis based on the 1st law of thermodynamics -- Caloric Balance or Lipophilia -- will win? If it can be shown that 'a calorie is a calorie' irrespective of what you eat, then Caloric Balance wins. If not, Lipophilia wins.