  Entropic uncertainty relations play an important role in both fundamentals
and applications of quantum theory. Although they have been well-investigated
in quantum theory, little is known about entropic uncertainty in generalized
probabilistic theories (GPTs). The current study explores two types of entropic
uncertainty relations, preparation and measurement uncertainty relations, in a
class of GPTs which can be considered generalizations of quantum theory. Not
only a method for obtaining entropic preparation uncertainty relations but also
an entropic measurement uncertainty relation similar to the quantum one by
Buscemi et al. [Phys. Rev. Lett., 112, 050401] are proved in those theories. It
manifests that the entropic structure of uncertainty relations in quantum
theory is more universal. Concrete calculations of our relations in GPTs called
the regular polygon theories are also demonstrated.
