  In this paper we explore collisional ionization and time-evolving
photoionization in the, X-ray discovered, ionized absorbers in Seyfert
galaxies. These absorbers show temporal changes inconsistent with simple
equilibrium models. We develop a simple code to follow the temporal evolution
of non-equilibrium photoionized gas. As a result several effects appear that
are easily observable; and which, in fact, may explain otherwise paradoxical
behavior.
  Specifically we find that: 1) In many important astrophysical conditions pure
collisional and photoionization equilibria can be distinguished with moderate
spectral resolution observations, due to a strong absorption structure between
1 and 3 keV. 2) In time-evolving non-equilibrium photoionization models the
response of the ionization state of the gas to sudden changes of the ionizing
continuum is smoothed and delayed at low gas densities, even when the
luminosity increases. 3) If the changes of the ionizing luminosity are not
instantaneous, and the electron density is low enough (the limit depends on the
average ionization state of the gas), the ionization state of the gas can
continue to increase while the source luminosity decreases, so a maximum in the
ionization state of a given element may occur during a minimum of the ionizing
intensity (the opposite of the prediction of equilibrium models). 4) Different
ions of different elements reach their equilibrium configuration on different
time-scales.
  These properties are similar to those seen in several ionized absorbers in
AGN, properties which had hitherto been puzzling. We applied these models to a
high S/N ROSAT PSPC observation of the Seyfert 1 galaxy NGC 4051.
