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PreprintCC BY 4.0arXiv

Grand Canonical Generators

  • Andreas Burger
  • Malte Franke
  • Luka Mucko
  • Kjell Jorner
  • Alan Aspuru-Guzik
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Abstract

We introduce Grand Canonical Generators (GCG), a generative framework that extends Boltzmann generators to the grand canonical ensemble. We present two designs. The first conditions a variable-size generative model on the chemical potential, sampling particle number and configuration jointly. The second factorizes the grand canonical distribution into a particle-number distribution and the corresponding canonical Boltzmann density. This factorized formulation can use any existing Boltzmann generator for the canonical component, encodes the known linear chemical-potential dependence analytically, and yields a tractable likelihood that supports self-normalized importance sampling (SNIS). Empirically, GCG accurately reproduces grand canonical observables on a Lennard--Jones fluid and methane adsorption in a zeolite, demonstrating generalization across chemical potentials and correction via SNIS and grand canonical Monte Carlo.

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Cite

BibTeXRIS
BibTeX
@misc{burger2026grand,
  title = {{Grand Canonical Generators}},
  author = {Andreas Burger and Malte Franke and Luka Mucko and Kjell Jorner and Alan Aspuru-Guzik},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00683},
  eprint = {2610.00683},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00683},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Grand Canonical Generators
AU  - Andreas Burger
AU  - Malte Franke
AU  - Luka Mucko
AU  - Kjell Jorner
AU  - Alan Aspuru-Guzik
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.00683
UR  - https://arxiv.org/abs/2610.00683
AB  - We introduce Grand Canonical Generators (GCG), a generative framework that extends Boltzmann generators to the grand canonical ensemble. We present two designs. The first conditions a variable-size generative model on the chemical potential, sampling particle number and configuration jointly. The second factorizes the grand canonical distribution into a particle-number distribution and the corresponding canonical Boltzmann density. This factorized formulation can use any existing Boltzmann generator for the canonical component, encodes the known linear chemical-potential dependence analytically, and yields a tractable likelihood that supports self-normalized importance sampling (SNIS). Empirically, GCG accurately reproduces grand canonical observables on a Lennard--Jones fluid and methane adsorption in a zeolite, demonstrating generalization across chemical potentials and correction via SNIS and grand canonical Monte Carlo.
ER  -