  Soft-pion theorems are used to show how chiral symmetry constrains the
contributions of low-momentum pions to the quark condensate, the pion decay
constant and hadron masses, all of which have been proposed as signals of
partial restoration of chiral symmetry in matter. These have contributions of
order T^2 for a pion gas or of order m_pi for cold nuclear matter, which have
different coefficients in all three cases, showing that there are no simple
relations between the changes to these quantities in matter. In particular,
such contributions are absent from the masses of vector mesons and nucleons and
so these masses cannot scale as any simple function of the quark condensate.
More generally, pieces of the quark condensate that arise from low-momentum
pions should not be associated with partial restoration of chiral symmetry.
