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PreprintCC BY 4.0arXiv

Global equilibrium at order π’ͺ(ℏ2): pseudo-gauge ambiguity, Maxwell relations, and thermodynamic consistency

  • Asaad Daher
  • David Wagner
  • Masoud Shokri
  • Dirk H. Rischke
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Abstract

We study massive spin-1/2 Boltzmann particles in global thermodynamic equilibrium with rotation and acceleration, consistently including quantum corrections up to order π’ͺ(ℏ2). 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 k2 = m2 is modified at order π’ͺ(ℏ2) 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.

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Cite

BibTeXRIS
BibTeX
@misc{daher2026global,
  title = {{Global equilibrium at order $\mathcalO(\hbar^2)$: pseudo-gauge ambiguity, Maxwell relations, and thermodynamic consistency}},
  author = {Asaad Daher and David Wagner and Masoud Shokri and Dirk H. Rischke},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31819},
  eprint = {2609.31819},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31819},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Global equilibrium at order π’ͺ(ℏ^2): pseudo-gauge ambiguity, Maxwell relations, and thermodynamic consistency
AU  - Asaad Daher
AU  - David Wagner
AU  - Masoud Shokri
AU  - Dirk H. Rischke
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31819
UR  - https://arxiv.org/abs/2609.31819
AB  - We study massive spin-1/2 Boltzmann particles in global thermodynamic equilibrium with rotation and acceleration, consistently including quantum corrections up to order π’ͺ(ℏ^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 π’ͺ(ℏ^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.
ER  -