Notes toward a Newtonian thermodynamics

We interpret the moment generating function $\mathbf{E}(e^{tX}):={\mathrm{e}\mathrm{x}\mathrm{p}}_F(t)\in \mathbf{R}[[t]]$ of a random variable $X$ as the exponential of an associated one-dimensional formal group law $F$ defined over $\mathbf{R}$.