  We present a general definition of entropy in the setting of pre-ordered
semigroups, extending the notion of topological entropy. From our definition,
we obtain the basic properties exhibited by various entropy-like theories
encountered in the literature, many of them being particular cases of our
scheme. We show how to derive from the properties of the abstract entropy
corresponding properties in the concrete cases. We also introduce a notion of
expansiveness in this general context, extending the concept of expansive
dynamical system, which is related to the entropy in a similar fashion as in
the case of topological dynamics. Finally, as an application, we suggest some
definitions of new entropies and expansiveness in concrete cases.
