Captain reported loss off thrust with the #2 Engine resulted in an in flight shut down of the affected engine. The flight crew diverted and began fuel jettison procedures and a subsequent overweight landing was made at the diversion airport.

Narrative

Climbing out of FL200 I noticed that the number 2 engine was not developing the same power as the other 3 engines. I checked the 3 engine optimum altitude and requested to level off at FL 260 which was approved. Within the next 50 minutes; the # 2 engine was producing less and less power until it was producing only idle power. I informed the Company that I would shut down the # 2 engine to prevent any further damage per the Quick Reference Handbook; Engine Limit or Surge or Stall checklist. The flight continued on the original route until the company requested that our flight divert to our maintenance base at ZZZ1. We accepted a new route to a fix over the ZZZZZ where we descended to FL150; entered holding and began fuel jettison. The fuel jettison worked normal for the first 60 tons dumped; but shut off prematurely and we could not jettison any more fuel per the procedure. We than had to lower the gear and extend flaps to increase the fuel burn while in the holding pattern to reach our maximum landing weight. Upon knowing that we could land safely under the max landing weight; we exited the hold and proceeded to make a normal approach and 3 engine landing. At block in; both the # 2 engine irregularities and fuel jettison irregularity were entered into the maintenance logbook. The flight crew of 4 worked well as a team; and the company dispatch gave us the appropriate information as we needed it.