In first-order cosmological phase transitions, the asymptotic velocity of expanding bubbles is of crucial relevance for predicting observables like the spectrum of stochastic gravitational waves, or for establishing the viability of mechanisms explaining fundamental properties of the universe such as the observed baryon asymmetry. In these dynamic phase transitions, it is generally accepted that subluminal bubble expansion requires out-of-equilibrium interactions with the plasma which are captured by friction terms in the equations of motion for the scalar field. This has been disputed in works pointing out subluminal velocities in local equilibrium arising either from hydrodynamic effects in deflagrations or from the entropy change across the bubble wall in general situations. We argue that both effects are related and can be understood from the conservation of the entropy of the degrees of freedom in local equilibrium, leading to subluminal speeds for both deflagrations and detonations. The friction effect arises from the background field dependence of the entropy density in the plasma, and can be accounted for by simply imposing local conservation of stress-energy and including field dependent thermal contributions to the effective potential. We illustrate this with explicit calculations of dynamic and static bubbles for a first-order electroweak transition in a Standard Model extension with additional scalar fields.

在一阶宇宙相变中，膨胀气泡的渐近速度对于预测诸如随机引力波谱之类的可观测物，或者对于建立解释宇宙基本特性（如观测到的重子不对称）的机制的可行性至关重要。在这些动态相变中，人们普遍认为，腔下气泡膨胀需要与等离子体的不平衡相互作用，这由标量场运动方程中的摩擦项捕获。这在指出局部平衡中的亚光速速度是由爆燃中的流体动力学效应或在一般情况下穿过气泡壁的熵变化引起的工作中存在争议。我们认为这两种效应是相关的，并且可以从局部平衡中自由度的熵守恒来理解，从而导致爆燃和爆炸的亚光速。摩擦效应源于等离子体中熵密度的背景场依赖性，并且可以通过简单地施加局部应力能量守恒和包括场依赖性热对有效势的贡献来解释。我们通过对具有附加标量场的标准模型扩展中的一阶电弱跃迁的动态和静态气泡的显式计算来说明这一点。摩擦效应源于等离子体中熵密度的背景场依赖性，并且可以通过简单地施加局部应力能量守恒和包括场依赖性热对有效势的贡献来解释。我们通过对具有附加标量场的标准模型扩展中的一阶电弱跃迁的动态和静态气泡的显式计算来说明这一点。摩擦效应源于等离子体中熵密度的背景场依赖性，并且可以通过简单地施加局部应力能量守恒和包括场依赖性热对有效势的贡献来解释。我们通过对具有附加标量场的标准模型扩展中的一阶电弱跃迁的动态和静态气泡的显式计算来说明这一点。