We have previously presented arguments that there is no violation of physical principles [2,7] and, ironically, that suggesting a change in body mass to be independent of macronutrient composition would itself be a violation of the second law of thermodynamics [7]. Here, we reframe these arguments in a more pedagogically direct way and we provide simple examples.
The misunderstanding that continues to be repeated in the expression "a calorie is a calorie" appears to be exclusive reference to the first law of thermodynamics. The difficulty with this theoretical approach is that it is only part of the relevant physics and its relationship to biologic systems. The first law says that in any transformation the total energy in the system can be accounted for by the heat added to the system, the work done by the system on its environment and the change in energy content of all the components of the system. It is important to understand, however, that the first law does not say what the relative distribution between these effects will be for any process. In fact, the first law does not even allow us to say whether the process will occur at all. To understand the progress of a physical change it is necessary to understand the second law which introduces an entity known as the entropy, S, a measure of disorder in all processes. In all real (irreversible) processes, entropy increases, usually written ΔS > 0. The most common marker of increasing entropy is heat, although it is by no means the only evidence for increased entropy.
In systems at constant temperature and pressure (i.e. biologic systems)), the first and second law are combined in the Gibbs Free Energy, ΔG, which represents the maximum useful work that can be performed by the process. The actual process however, in general derives less useful work than permitted by the theoretically available ΔG due to inefficiency in energy capture. A proper accounting of entropy and efficiency must be included if we are to understand energy utilization in biological and biochemical systems.
Biological systems and thermodynamics
It is also important in the discussion of biological systems to understand that they are open systems, i.e. they take in nutrients and oxygen and excrete carbon dioxide, water, urea and other waste products, as well as heat. The importance with respect to weight considerations is that mass and energy are conserved (the more general statement of the first law of thermodynamics), but they are not conserved entirely within the organism.
To illustrate the proper interpretation of the first law of thermodynamics consider a subject whose resting energy expenditure is met by the production of 95 moles of ATP. Since oxidation of a single mole of glucose provides 38 moles of ATP, 2.5 moles of glucose will be needed to meet this individual's resting energy requirements. It is important to note that the resultant carbon dioxide, water, and heat are not retained within the organism. The useful retained energy is in the 95 moles of ATP (Figure 1B). (Similar equations could be written for lipid or protein but we restrict our discussion to glucose for simplicity).