  We reveal that the universal scaling properties of the chiral phase
transition in quantum chromodynamics (QCD) at the macroscale are, in fact,
encoded within the microscopic energy levels of its fundamental constituents,
the quarks. We introduce a novel relation between the cumulants of the chiral
order parameter, i.e., the chiral condensate, and the correlations among the
energy levels of quarks, i.e., the eigenspectra of the massless QCD Dirac
operator. This relation elucidates how the fluctuations of the chiral
condensate arise from the correlations within the infrared part of the energy
spectra of quarks, and naturally leads to a generalization of the Banks-Casher
relation for the cumulants of the chiral condensate. Then, through (2+1)-flavor
lattice QCD calculations using HISQ action with varying light quark masses
around the chiral phase transition temperature, we demonstrate that the
correlations among the infrared part of the Dirac eigenvalue spectra exhibit
same universal scaling behaviors as expected of the cumulants of the chiral
condensate. We find that these universal scaling behaviors extend up to the
physical values of the up and down quark masses.
