  We investigate bipartite particle number fluctuations near the rank-$2$
exceptional points (EPs) of $\mathcal{PT}$-symmetric Su-Schrieffer-Heeger
models. Beyond a conformal field theory of massless fermions, fluctuations or
equivalently compressibility is negative definite and exhibits superinflation
in leading order at EPs, due to the defectiveness in the biorthogonal Hilbert
space. Associated with the bipartite von Neumann entanglement entropy, a
parameter in an anomalous correspondence referencing from a purely
non-Hermitian limit helps characterize two inequivalent EP sets. Our work paves
the way for understanding the singularity of fluctuations relevant to EPs, more
promisingly detectable in experiments.
