  The amount of axial charge produced in heavy ion collisions is one of the key
quantities in understanding chiral magnetic effect. Current phenomenological
studies assume large axial charge chemical potential $\mu_5$ produced in Glasma
phase and assume the conservation of axial charge throughout the evolution,
which is valid in the long relaxation time limit. Based on the solution of
stochastic hydrodynamics with phenomenological parameters, our study suggests
that the situation of heavy ion collisions may be close to the opposite limit,
in which axial charge fluctuation approaches thermodynamic limit. Using $\mu_5$
set by the thermodynamic limit for chiral magnetic effect and a background from
parity-even $v_1$, we obtain a reasonable description of the centrality
dependence of charged particle correlation measured in experiment.
