<p>We investigate the hydrodynamic solutions for expanding bubbles in cosmological first-order phase transitions going beyond local thermal equilibrium approximation. Under the assumption of a tangensoidal field profile, we supplement the matching conditions with the entropy produced due to the interaction of the bubble wall with ambient plasma. This allows us to analytically compute the corresponding fluid profiles and find the bubble-wall velocity. We show that due to the entropy production, two stable solutions corresponding to a deflagration or hybrid and a detonation can coexist. Finally, we use numerical real-time simulations of bubble growth to show that in such cases it is typically the faster detonation solution which is realised. This effect can be explained in terms of the fluid profile not being fully formed into the predicted steady-state solution as the wall accelerates past this slower solution.</p>