  This paper is motivated by the recent paper M. Baldovin, S. Iubini, R. Livi
and A. Vulpiani, Statistical mechanics of systems with negative temperature,
arXiv:2103.12572. The authors suggest that negative absolute temperatures are
consistent with equilibrium thermodynamics. This is correct, if the environment
also has negative temperature. Otherwise such states represent the transient
though maybe long-lived metastable effects. Here we consider the extension of
the negative temperatures to the relativistic systems. We show that the
negative state is possible in the Dirac vacuum, which is obtained by the $PT$
symmetry transformation from the conventional Dirac sea. If such vacuum with
inverse population fills the whole Universe, its thermodynamics determined by
negative temperatures becomes equilibrium.
