Just out of curiosity, I'm trying to get a sense of the order-of-magnitude theoretical thermodynamic cost of food absorbtion. I'm thinking of food absorption as "move nutrients in newly consumed food to their desired location in the body". I am just wondering if this way of estimating it is broadly correct.
Assume that a piece of food enters the small intestine from the stomach, and approximate it as a fully mixed ideal gas consisting of all the various nutrients.
Assume the nutrients have already been broken down into their constituent parts, and the cost of this is zero.
Assume each nutrient has to move to some particular location in the body (possibly spread out over all the cells in the body). Assume this is thermodynamically equivalent to simply separating the nutrients in the food (once they are separated, they can be moved to their target locations without decreasing their entropy).
Using these assumptions, the thermodynamic cost is simply the cost of separating mixed ideal gases of nutrients. Let's assume we just have 3 nutrients and water, in equal proportions (glucose, fatty acids, amino acids, and water, each 25% of the volume), and lets assume 300 Kelvin. Then we get that the energy cost of separating 1 mole of each of these ideal gases is given by $\Delta E=300*N_A*k_B*log(4)\approx 300*6*2J=3600J=3.6kJ$.
(E.g. one mole of glucose weighs 180 grams, which has a nutritional content of about $3000kJ$, so the lower-limit thermodynamic cost of "absorbing" glucose from food under these assumptions is about 0.1% of the energy content of that glucose.)
Is this kind of reasoning basically right, for an order-of-magnitude estimate? Or am I missing something fundamental about digestion and so on?