  The proof of the existence of the thermodynamic limit for electrons and
nuclei interacting via the Coulomb potential, in the framework of
non-relativistic quantum mechanics, was accomplished decades ago. This result
did not take account of interactions caused by magnetic fields, however, (the
spin-spin interaction, in particular) or of the quantized nature of the
electromagnetic field. Recent progress has made it possible to undertake such a
proof in the context of non-relativistic QED. This paper contains one part of
such a proof by giving a lower bound to the free energy which is proportional
to the number of particles and which takes account of the fact that the field,
unlike the particles, is never confined to a finite volume. In the earlier
proof the lower bound was a `two line' corollary of the `stability of matter'.
In QED the proof is much more complicated.
