Entropy production at electroweak bubble walls from scalar field fluctuations

TL;DR

This paper investigates entropy production at electroweak bubble walls due to scalar field fluctuations, revealing non-zero entropy discontinuity even with zero friction, challenging LTE assumptions and impacting bubble wall velocity limits.

Contribution

It introduces a Langevin dynamics framework to quantify entropy production from scalar fluctuations at electroweak bubble walls, showing non-vanishing entropy discontinuity in the zero friction limit.

Findings

Entropy production remains non-zero when friction approaches zero.

The entropy discontinuity is linked to the ballistic regime in Boltzmann equations.

LTE-based bounds on bubble wall velocity cannot be saturated.

Abstract

The real-time dynamics of an electroweak phase transition involves large time and distance scales, the domain of hydrodynamics. However, the matching conditions of ideal hydrodynamics across a bubble wall do not fix the fluid profile completely, with the remaining degree of freedom parametrizable through entropy production. Within a framework of Langevin dynamics, viewed as an effective description valid between the hydrodynamic ($k \sim g^4_{ } T/\pi^3_{ }$) and soft momentum scales ($k \sim gT$), we determine the entropy production originating from scalar field fluctuations. The entropy discontinuity is shown to remain non-vanishing when the friction coefficient is sent to zero, in apparent violation of the ``local thermal equilibrium'' (LTE) framework. To confirm the finding, we identify its origin within Boltzmann equations, as being part of the $1\to 1$ force associated with the ``ballistic'' regime. The result implies that LTE-based upper bounds on the wall velocity cannot be saturated.