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PreprintCC BY 4.0arXiv

The Scale Invariance Behind Boltzmann Counting

  • M. H. Benetti
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Abstract

Boltzmann counting possesses an exact scale invariance from which the specific entropy emerges without asymptotic approximation. Under thermodynamic replication, this invariance exposes the Gibbs excess at the multinomial level. Its resolution reveals a state-dependent scale structure whose additive refinement generates a continuum reference measure, giving a combinatorial origin to the reference structure of continuous statistical mechanics. The resulting entropy is relative to this measure, and for an ideal gas the scales acquire operational meaning through reversible work.

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Cite

BibTeXRIS
BibTeX
@misc{benetti2026scale,
  title = {{The Scale Invariance Behind Boltzmann Counting}},
  author = {M. H. Benetti},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30300},
  eprint = {2609.30300},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30300},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Scale Invariance Behind Boltzmann Counting
AU  - M. H. Benetti
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.30300
UR  - https://arxiv.org/abs/2609.30300
AB  - Boltzmann counting possesses an exact scale invariance from which the specific entropy emerges without asymptotic approximation. Under thermodynamic replication, this invariance exposes the Gibbs excess at the multinomial level. Its resolution reveals a state-dependent scale structure whose additive refinement generates a continuum reference measure, giving a combinatorial origin to the reference structure of continuous statistical mechanics. The resulting entropy is relative to this measure, and for an ideal gas the scales acquire operational meaning through reversible work.
ER  -