Entropy production at electroweak bubble walls from scalar field fluctuations

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 ($k \sim g^4_{ } T/π^3_{ }$) 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.