{
  "abstract": "We study massive spin-$1/2$ Boltzmann particles in global thermodynamic equilibrium with rotation and acceleration, consistently including quantum corrections up to order $\\mathcal{O}(\\hbar^2)$. For such a system, the fluid velocity becomes an independent thermodynamic variable and fundamental thermodynamic relations have to be extended. Employing the Wigner-function formalism, we show that the standard mass-shell condition $k^2 = m^2$ is modified at order $\\mathcal{O}(\\hbar^2)$ by contributions quadratic in the thermal vorticity. Incorporating this modified mass-shell constraint, we derive the (net) particle-number current, energy-momentum tensor, spin-current tensor, and associated thermodynamic quantities in the kinetic, canonical, and de Groot--van Leeuwen--van Weert (GLW) pseudo-gauges. We explicitly demonstrate that, while global quantities, like the total particle number or total energy, are independent of the choice of pseudo-gauge, local quantities, like the particle-number density or the energy density, are pseudo-gauge dependent. We then examine the thermodynamic relations in each pseudo-gauge and demonstrate that thermodynamic consistency requires that the thermodynamic Maxwell relations are satisfied. We find that these relations hold in the kinetic-theory pseudo-gauge, whereas they are in general violated in the canonical and GLW pseudo-gauges. These findings suggest a preference for using the kinetic-theory pseudo-gauge in applications such as spin hydrodynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31819",
  "author_total": 4,
  "authors": [
    {
      "name": "Asaad Daher"
    },
    {
      "name": "David Wagner"
    },
    {
      "name": "Masoud Shokri"
    },
    {
      "name": "Dirk H. Rischke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fhr2scykaqate.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31819",
  "fulltext_url": null,
  "id": "fhr2scykaqate",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31819",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "openalex",
      "3106|High-Energy Particle Collisions Research"
    ]
  ],
  "openalex": "W7214786055",
  "pdf_url": "https://arxiv.org/pdf/2609.31819",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fhr2scykaqate.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.31819",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31819"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Global equilibrium at order $\\mathcal{O}(\\hbar^2)$: pseudo-gauge ambiguity, Maxwell relations, and thermodynamic consistency",
  "title_text": "Global equilibrium at order 𝒪(ℏ^2): pseudo-gauge ambiguity, Maxwell relations, and thermodynamic consistency",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/fhr2scykaqate",
  "venue": "arXiv",
  "versions": []
}