The Statistical Mechanics of Human Weight Change

TL;DR

This paper develops a statistical mechanics model for human BMI dynamics, revealing how weight changes are driven by drift towards the mean and BMI-proportional fluctuations, explaining distribution broadening and social influence effects.

Contribution

It introduces a novel stochastic model for BMI changes, linking physical science concepts to human weight dynamics and providing quantitative insights into obesity trends.

Findings

Heavy individuals tend to lose weight on average.

Light individuals tend to gain weight on average.

BMI distribution broadens over time due to proportional fluctuations.

Abstract

In the context of the global obesity epidemic, it is important to know who becomes obese and why. However, the processes that determine the changing shape of Body Mass Index (BMI) distributions in high-income societies are not well-understood. Here we establish the statistical mechanics of human weight change, providing a fundamental new understanding of human weight distributions. By compiling and analysing the largest data set so far of year-over-year BMI changes, we find, strikingly, that heavy people on average strongly decrease their weight year-over-year, and light people increase their weight. This drift towards the centre of the BMI distribution is balanced by diffusion resulting from random fluctuations in diet and physical activity that are, notably, proportional in size to BMI. We formulate a stochastic mathematical model for BMI dynamics, deriving a theoretical shape for the BMI distribution and offering a mechanism to explain the ongoing right-skewed broadening of BMI distributions over time. The model also provides new quantitative support for the hypothesis that peer-to-peer social influence plays a measurable role in BMI dynamics. More broadly, our results demonstrate a remarkable analogy with drift-diffusion mechanisms that are well-known from the physical sciences and finance.