strings do not make time in ordinary string theory. They exist in spacetime and participate in the time from that. I don't know about decaying vibrations in strings. In fact I think it's only recently that anyone has worked on strings at a finite temperature, where you might discuss entropy. This is all just a rumor to me, perhaps someone more learned will chip in.
I think it depends on if time is relative. Does time require measurement or does it exist outside of that measurement?
Has anyone thought to define time in terms of string theory? Or is it taken for granted and still measured as it is?
time in string theory
Just posted a thread of defining time in string theory. The title is "minimum time" and its found in this (Strings, Branes and LQG) forum. In gist, the smallest unit of time is the Planck time (defined as the amount of time it takes light to travel a Planck distance). Since a string is a Planck length in size, it cannot fit into a smaller space. Therefore, when a photon travels through a Planck distance, it takes up the whole space and can only be defined as a whole string within that amount of time, no less. In other words, if all matter is manifested as a vibrating string, it cannot exist without defining a whole string.