turning amp on vs tweater hiss

I've been had my amp turned on since last week. While I was walking by my speakers, I just noticed the fact that even without any music playing, if the amp is turned on, hiss comes out from the tweaters.

Now, with my amp left on music sounds better, but in addition tweaters will get signal (which generates hiss) 24/7. Is it going to damage the tweaters in anyway?

Should I continue to leave my amp on or not?