At the moment I have my Mac mini connected to my amplifier through HDMI. The volume button is grayed out so I can only adjust through my amplifier. The problem is the mini is significantly louder than TV, BluRay etc so I need to constantly adjust the volume when switching between devices. Is there any way to turn the volume of the mini down when connected to an external device?
Data, including video and audio, is sent over the HDMI cable in digital form, not analog. The only way you could adjust that would be to adjust the content of the digital data, which is a destructive operation.
Depending on the software used it is also possible that your machine is sending compressed data, such as AC3 or DTS audio, directly to the receiver which decodes it.
Generally the solution is on the receiver side, which often has a "source volume" adjustment option.