Notes toward a Newtonian thermodynamics

Abstract

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

The cumulant generating functions of statistical mechanics are closely related to Gibbs free energy in thermodynamics, and in turn to classical symmetric and partition functions, and through them to formal groups and the characteristic classes of VL Ginsburg's (pre-quantized) symplectic manifolds