  Non-Hermitian systems with exceptional points lead to many intriguing
phenomena due to the coalescence of both eigenvalues and corresponding
eigenvectors, in comparison to Hermitian systems where only eigenvalues
degenerate. In this paper, we have investigated entropic uncertainty relation
(EUR) in a non-Hermitian system and revealed a general connection between the
EUR and the exceptional points of non-Hermitian system. Compared to the
unitarity dynamics determined by a Hermitian Hamiltonian, the behaviors of EUR
can be well defined in two different ways depending on whether the system is
located in unbroken phase or broken phase regimes. In unbroken phase regime,
EUR undergoes an oscillatory behavior while in broken phase regime where the
oscillation of EUR breaks down. The exceptional points mark the oscillatory and
non-oscillatory behaviors of the EUR. In the dynamical limit, we have
identified the witness of critical behavior of non-Hermitian systems in terms
of the EUR. Our results reveal that the witness can detect exactly the critical
points of non-Hermitian systems beyond (anti-) PT-symmetric systems. Our
results may have potential applications to witness and detect phase transition
in non-Hermitian systems.
