  We develop a model to calculate strangeness production in both elementary and
heavy ion collisions, within the framework of a statistical approach to
hadronisation. Calculations are based on the canonical partition function of
the thermal Nambu-Jona-Lasinio model with exact conservation of flavor and
color. It turns out that the growth of strange quarks production in heavy ion
collisions is due to the initial excess of non-strange matter over antimatter,
whereas a suppression occurs for elementary collisions, owing to the constraint
of exact quantum charges conservation over small volumes.
