Let $(X,d)$ be a compact metric space and f a continuous transformation on X. f has the specification if one can always find a single orbit to interpolate between different pieces of orbits, up to a preassigned error. We call the map $\mu \to h_{\mu}(f)$ (KolmogorovSinai entropy) the entropy map . Does specification implies that entropy map is upper semicontinuous?

Expansivity implies that the entropy map is upper semicontinuous. See P. walters book Thm 8.2. I think that if the shadowing orbit in your definition of specification is unique then the map f is expansive. 

