  In the large $N$ limit a physical system might acquire a residual entropy at
zero temperature even without ground state degeneracy. At the same time poles
in the 2-point function might coalesce and form a branch cut. Both phenomena
are related to a high density of states in the large $N$ limit. In this short
note we address the question: does a branch cut in the 2-point function always
lead to non-zero residual entropy? We argue that for generic fermionic systems
in $0+1$ dimensions in the mean-field approximation the answer is positive:
branch cut $1/\tau^{2\Delta}$ in the 2-point function does lead to a lower
bound $N \log{2}(1/2-\Delta)$ for the entropy. We also comment on
higher-dimensional generalizations and relations to the holographic
correspondence.
