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  • Letter
  • Open Access

Accurate and thermodynamically consistent hydrogen equation of state for planetary modeling with flow matching

Hao Xie*, Saburo Howard, and Guglielmo Mazzola†

  • *Contact author: qwexiehao@gmail.com
  • †Contact author: guglielmo.mazzola@uzh.ch
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Phys. Rev. Research 7, L032028 – Published 7 August, 2025

DOI: https://doi.org/10.1103/n1jt-r2rj

Abstract

Accurate determination of the equation of state of dense hydrogen is essential for understanding gas giants. Currently, there is still no consensus on methods for calculating its entropy, which play a fundamental role and can result in qualitatively different predictions for Jupiter’s interior. Here, we investigate various aspects of entropy calculation for dense hydrogen based on ab initio molecular dynamics simulations. Specifically, we employ the recently developed flow matching method to validate the accuracy of the traditional thermodynamic integration approach. We then clearly identify pitfalls in previous attempts and propose a reliable framework for constructing the hydrogen equation of state, which is accurate and thermodynamically consistent across a wide range of temperature and pressure conditions. This allows us to conclusively address the long-standing discrepancies in Jupiter’s adiabat among earlier studies, demonstrating the potential of our approach for providing reliable equations of state of diverse materials.

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Phys. Rev. Research 7, L032028– Published 7 August, 2025
  • Received 25 November 2024
  • Accepted 12 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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