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arXiv · 2610.16385

Nonequilibrium framework for first-order phase transitions

Jie Liu·Ligong Bian
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Abstract

The first-order phase transition is central to electroweak baryogenesis and gravitational wave generation, yet thermal equilibrium effective potential analyses cannot describe the real-time non-equilibrium dynamics of the phase transition process. We use the Schwinger-Keldysh closed-time-path formalism of real-time finite-temperature field theory to study these effects. For the $ϕ^6$ model, we derive the effective action and the corresponding Langevin equation. We further extend the formalism to the two scalar fields case, obtaining the coupled Langevin equations. These results provide a theoretical framework for the bubble nucleation simulation of the non-equilibrium phase transition process, laying the foundation for reliable predictions of baryogenesis and gravitational wave signals.

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Jie Liu, Ligong Bian. 2026-10-12. Nonequilibrium framework for first-order phase transitions. https://arxiv.org/abs/2610.16385

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