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

TL;DR

This paper develops a reliable, thermodynamically consistent hydrogen equation of state using flow matching and ab initio simulations, resolving discrepancies in planetary models of gas giants like Jupiter.

Contribution

It introduces a new framework combining flow matching with molecular dynamics to accurately determine hydrogen's thermodynamic properties for planetary modeling.

Findings

Validated traditional thermodynamic integration with flow matching

Identified pitfalls in previous entropy calculations

Provided a consistent hydrogen equation of state across conditions

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.