How to turn off my speakers when no sound is being played?
You describe the problem as having 11.8 watt on the speakers while there is no sound coming from them. 
Try using Mute, to make sure no sound output is send to the speakers.

You also say you have 2 sound outputs one to the monitor via HDMI for the system sounds on external monitor the other to your external speakers true the headphone jack. 

That is possible but requires special settings in the System Audio or 3D party audio application.

It is not possible to have 11.8 watt (as measured by your wattmeter) of audio power going to speakers without them making any noise, unless the speakers audio amplifier is junk. 

It is possible that your speakers draw power because they have defective audio amplifier. I suggest looking in to it or returning the product.