Allostery plays a fundamental role in most biological processes. However, little theory is available to describe it outside of two-state models. Here we use a statistical mechanical approach to show that the allosteric coupling between two collective variables is not a single number, but instead a two-dimensional thermodynamic coupling function that is directly related to the mutual information from information theory and the copula density function from probability theory. On this basis, we demonstrate how to quantify the contribution of specific energy terms to this thermodynamic coupling function, enabling an approximate decomposition that reveals the mechanism of allostery. We illustrate the thermodynamic coupling function and its use by showing how allosteric coupling in the alanine dipeptide molecule contributes to the overall shape of the Φ/Ψ free energy surface, and by identifying the interactions that are necessary for this coupling.