this sounds like degeneracy pressure. The neutrons have spin 1/2, so they must obey the Pauli exclusion principle... unless they are unrealistically cold, much less than 10^-30K or something ridiculous like that, then they form bosonic pairs and behave like bosons, much like what electrons do at low energies in a superconductor (my thermal physics prof. told me the gist of a paper that another prof. wrote at the U of M). For all practical purposes, neutrons will always obey the Pauli exclusion principle, and hence we can speak of things such as "degeneracy pressure", but as far as I know, there simply is no "energy emission". Perhaps you mean energy transfer in the form of sound waves, light, collisions and the sort? As long as the system has a temperature gradient, there will always be energy transfer which will serve to bring the system in equilibrium.