Quantitative Foundations of Energy Balance Are Not Empirically Reliable Under Ideal Conditions

Quantitative models must reproduce empirical data with small, reproducible errors when their governing equations are supplied with accurately measured inputs. The Energy Balance Model (EBM) of human bodyweight regulation is widely treated as such, yet its numerical and logical consistency has rarely been tested under suitably rigorous conditions. This article reassesses the validity of the EBM by applying three numerical consistency tests, derived directly from its governing principles, to metabolic-ward data from two influential randomized controlled trials. The first test evaluates whether average energy balance computed from changes in body composition agrees with average energy balance computed as absorbed energy intake minus energy expenditure. The second test examines whether individuals with similar body mass energy densities and energy imbalances exhibit comparable weight changes. The third test assesses whether changes in fat mass equal the product of average daily fat balance and intervention duration. Across trials, the EBM fails all three tests: relative prediction errors range from about 20% to nearly 400%, the relationship between energy imbalance and weight change is weak and inconsistent, and half of the positive energy balance cases coincide with weight loss. Reanalysis within a mass balance framework, by contrast, reveals strong, systematic relationships between water-free food-mass intake, weight change, and diet composition. Theoretical examination further shows that equating energy balance with mass balance forces the EBM into a state in which body mass is simultaneously stable and decreasing, demonstrating internal self-contradiction and identifying the fundamental source of empirical and theoretical incoherence: in open systems, energy balance is not equivalent to mass balance. These findings indicate that the EBM functions as an empirical heuristic rather than a physically coherent model and instead support an appetite-regulated mass balance framework as a more appropriate basis for understanding bodyweight regulation and for evaluating hormonal-based theories such as the carbohydrate-insulin model.