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arXiv · 2512.22871

On the Cocycle Structure of the Boltzmann Distribution

Chuan-Tsung Chan·Chan-Yi Chang·Zhong-Tang Wu
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Abstract

Based on a cocycle structure, we identify a new derivation of the Boltzmann distribution for finite energy-level systems from the maximal entropy principle (MEP). Our approach does not rely on the method of the Lagrange multiplier, and it provides a more transparent way to understand the dependence on the energy levels of the temperature $T = 1/\beta$ for the equilibrium distribution. Finally, we make two curious observations associated with our derivations.

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Chuan-Tsung Chan, Chan-Yi Chang, Zhong-Tang Wu. 2025-12-28. On the Cocycle Structure of the Boltzmann Distribution. https://arxiv.org/abs/2512.22871

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