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<p>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.</p>

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On the origin of the Boltzmann distribution

  • 期刊论文

  • 发表日期：

    2025年8月17日

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  • Fedor Sandomirskiy,
  • Omer Tamuz

摘要

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.