The "J" is the latest iteration of the venerable C-130. Its RR AE2100 engines are limited to about 4000 hp each by the airframe but they can put out 4000 hp under any conditions. The previous models' Allison T-56 engines put out 4000hp under perfect conditions. The old T-56A-7 engines I worked on wouldn't hit rated power when fresh from the depot under standard day conditions.
http://www.takeofftube.com/view/4280/c130-extreme-demo/
http://www.takeofftube.com/view/4280/c130-extreme-demo/