  We prove that the topological entropy of any dominant rational self-map of a
projective variety defined over a complete non-Archimedean field is bounded
from above by the maximum of its dynamical degrees, thereby extending a theorem
of Gromov and Dinh-Sibony from the complex to the non-Archimedean setting. We
proceed by proving that any regular self-map which admits a regular extension
to a projective model defined over the valuation ring has necessarily zero
entropy. To this end we introduce the e-reduction of a Berkovich analytic
space, a notion of independent interest.
