  Density fluctuations resulting from spinodal decomposition in a
non-equilibrium first-order chiral phase transition are explored. We show that
such instabilities generate divergent fluctuations of conserved charges along
the isothermal spinodal lines appearing in the coexistence region. Thus,
divergent density fluctuations could be a signal not only for the critical end
point but also for the first order phase transition expected in strongly
interacting matter. We also compute the mean-field critical exponent at the
spinodal lines. Our analysis is performed in the mean-field approximation to
the NJL model formulated at finite temperature and density. However, our main
conclusions are expected to be generic and model independent.
