  In 2002, a method has been proposed by Buchholz et al. in the context of
Local Quantum Physics, to characterize states that are locally in thermodynamic
equilibrium. It could be shown for the model of massless bosons that these
states exhibit quite interesting properties. The mean phase-space density
satisfies a transport equation, and many of these states break time reversal
symmetry. Moreover, an explicit example of such a state, called the Hot Bang
state, could be found, which models the future of a temperature singularity.
However, although the general results carry over to the fermionic case easily,
the proof of existence of an analogue of the Hot Bang state is not quite that
straightforward. The proof will be given in this paper. Moreover, we will
discuss some of the mathematical subtleties which arise in the fermionic case.
