Symmetry restoration, Tunnelling and the Null Energy Condition

A finite volume allows tunnelling between degenerate vacua in Quantum Field Theory, and leads to remarkable energetic features, arising from the competition of different saddle points in the partition function. We describe this competition for finite temperature at equilibrium, taking into account both static and (Euclidean) time-dependent saddle points. The effective theory for the homogeneous order parameter yields a non-extensive vacuum energy at low temperatures, implying a dynamical violation of the Null Energy Condition.