On the origin of the Boltzmann distribution

Fedor Sandomirskiy; Omer Tamuz

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arXiv · 2307.11372

On the origin of the Boltzmann distribution

Fedor Sandomirskiy·Omer Tamuz

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Abstract

The family of Boltzmann distributions is used in statistical mechanics to describe the distribution of states in systems with 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.

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Fedor Sandomirskiy, Omer Tamuz. 2023-07-21. On the origin of the Boltzmann distribution. https://arxiv.org/abs/2307.11372

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