  To an exact endofunctor of a triangulated category with a split-generator,
the notion of entropy is given by Dimitrov-Haiden-Katzarkov-Kontsevich, which
is a (possibly negative infinite) real-valued function of a real variable. It
is important to evaluate the value of the entropy at zero in relation to the
topological entropy. In this paper, we study the entropy at zero of an exact
autoequivalence of the derived category of a complex smooth projective curve,
and prove that it coincides with the natural logarithm of the spectral radius
of the induced automorphism on its numerical Grothendieck group.
