With the help of a master equation we study the evolution of the
multiplicity distribution. Particularly we focus on the third and fourth
factorial moments from which all other kinds of moments can be
calculated. Among them we also determine the skewness and the kurtosis.
We first study how the third and the fourth moments thermalise when the
kinetic temperature is fixed. Then we study the evolution of the moments
in a situation with decreasing temperature. It is shown that the
relaxation time is the same for all moments but moments of higher orders
get initially further from the equilibrium value if temperature is
changed. We thus issue a warning flag on extraction of temperature from
the higher moments if they come from a rapidly cooling fireball.
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