The Asymmetric Accounting of Obligatory Nitrogen Loss: A Constructive Note on the Internal Consistency Proof of the Energy Balance Model

A recent paper by Arencibia-Albite presents an analytical proof that the Energy Balance Model (EBM) is internally inconsistent when obligatory non-urinary nitrogen losses are explicitly accounted for. The proof derives a negative protein balance and persistent carbohydrate accumulation under simultaneous energy balance and body weight stability. This commentary identifies a specific thermodynamic accounting issue in the proof: absorbed protein intake is credited with the full oxidative energy density on the intake side of the energy balance equation, while the chemical bond enthalpy carried out of the body by unoxidized nitrogen-containing material is omitted from the outflow side. When this enthalpy is explicitly included, consistent with the First Law of Thermodynamics for an open system, the contradiction resolves. The resolution is not a refutation of the paper's broader project. It is a refinement that strengthens the case for the Mass Balance Model (MBM) by showing that the EBM, when corrected, requires a mass-based term.