On tunneling at finite energies and temperatures

We study the contribution of finite energy tunneling to the total vacuum transition rate in a system at finite temperature. We find that in certain models, such as the 1+1 Abelian Higgs model, the quantum contribution is non-negligible even at large temperatures. We show how the persistence of the cosmological baryon asymmetry yields a bound on the inclusive two particle cross section in the anomalous (B violating) sector.