  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.
