The functional properties of the entropy gives rise to 6 possible types of thermodynamics. Additivity or superadditivity or subadditivity are closely related to extensivity and this is one of the characteristics used to distinguish the 6 types. We give examples some are somewhat academic of all of these, except one. For this purpose we draw also on black hole systems which h a ve been proposed. Some of these systems have subadditive e n tropies, i.e. they tend to fragment rather than clump.

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... r proposing a new entropy function we raise the problem of how to select from these entropy functions. Are some better than others?