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 ($k\sim g_{}^{4}T\mathrm{/}{\pi }_{}^3$) 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.