Abstract: "Boltzmann distributions are used in statistical mechanics to describe how the states of a system are distributed at a given temperature. We give a novel characterization of this family as the unique one satisfying independence for uncoupled systems. The theorem boils down to a statement about endomorphisms of the convolution semi-group of finitely supported probability measures on the natural numbers, or, alternatively, about endomorphisms of the multiplicative semi-group of polynomials with non-negative coefficients."
Original article: "On the origin of the Boltzmann distribution" - https://arxiv.org/abs/2307.11372
Abstract: "Boltzmann distributions are used in statistical mechanics to describe how the states of a system are distributed at a given temperature. We give a novel characterization of this family as the unique one satisfying independence for uncoupled systems. The theorem boils down to a statement about endomorphisms of the convolution semi-group of finitely supported probability measures on the natural numbers, or, alternatively, about endomorphisms of the multiplicative semi-group of polynomials with non-negative coefficients."