Thermal false vacuum decay is not what it seems

We study the decay of a thermally excited metastable vacuum in classical field theory using real-time numerical simulations. We find a lower decay rate than predicted by standard thermal theory. The discrepancy is due to the violation of thermal equilibrium during the critical bubble nucleation. It is reduced by introducing dissipation and noise. We propose a criterion for the system to remain in equilibrium during the nucleation process and show that it is violated in the Hamiltonian evolution of a single field. In the case of many fields, the fulfillment of the criterion is model-dependent.