  Proton-rich material in a state of nuclear statistical equilibrium (NSE) is
one of the least studied regimes of nucleosynthesis. One reason for this is
that after hydrogen burning, stellar evolution proceeds at conditions of equal
number of neutrons and protons or at a slight degree of neutron-richness.
Proton-rich nucleosynthesis in stars tends to occur only when hydrogen-rich
material that accretes onto a white dwarf or neutron star explodes, or when
neutrino interactions in the winds from a nascent proto-neutron star or
collapsar-disk drive the matter proton-rich prior to or during the
nucleosynthesis. In this paper we solve the NSE equations for a range of
proton-rich thermodynamic conditions. We show that cold proton-rich NSE is
qualitatively different from neutron-rich NSE. Instead of being dominated by
the Fe-peak nuclei with the largest binding energy per nucleon that have a
proton to nucleon ratio close to the prescribed electron fraction, NSE for
proton-rich material near freeze-out temperature is mainly composed of Ni56 and
free protons. Previous results of nuclear reaction network calculations rely on
this non-intuitive high proton abundance, which this paper will explain. We
show how the differences and especially the large fraction of free protons
arises from the minimization of the free energy as a result of a delicate
competition between the entropy and the nuclear binding energy.
