Is the same happen if you start a fresh 7.1.1?
If not there should be some configuration or deployment which do something.
You might monitor threads and take thread dumps to see what is active
Yes, the same thing happens with a brand new and untouched JBoss installation (7.1.1. Final). This time the memory starts from 16M and goes to 80M and then again and again. Is this something I should be worried about (is it a wanted behaviour)?
No, as if the server is idle there is still some activity and object are created. If the memory is not blown up and you did not see strong CPU use this is fine and a normal behaviour of Java applications