Super-heated first order phase transitions

We study first order phase transitions that occur when the temperature of the system increases and we identify the conditions that lead to super-heating, a phase where the system can heat up arbitrarily. First order phase transitions with super-heating behave as inverse transitions. We quantify these claims by studying a prototypical example of a dark sector with a large number of interacting light bosons at finite temperature. Depending upon thermalisation, a super-heated phase transition in cosmology is often associated with another transition when the system is eventually cooling down, enriching the spectrum of gravitational waves from bubble collisions.