  We study the driven dynamics across the critical points of the Yang-Lee edge
singularities (YLESes) in a finite-size quantum Ising chain with an imaginary
symmetry-breaking field. In contrast to the conventional classical or quantum
phase transitions, these phase transitions are induced by tuning the strength
of the dissipation in a non-Hermitian system and can occur even at finite size.
For conventional phase transitions, universal behaviors in driven dynamics
across critical points are usually described by the Kibble-Zurek mechanism,
which states that the scaling in dynamics is dictated by the critical exponents
associated with one critical point and topological defects will emerge after
the quench. While the mechanism leading to topological defects breaks down in
the YLES, we find that for small lattice size, the driven dynamics can still be
described by the Kibble-Zurek scaling with the exponents determined by the
$(0+1)$-dimensional YLES. For medium finite size, however, the driven dynamics
can be described by the Kibble-Zurek scaling with two sets of critical
exponents determined by both the $(0+1)$-dimensional and the
$(1+1)$-dimensional YLESes.
