Earlier quoted context omitted.
What is time, other than a state in which net entropy within a closed system increases (which is already a definition abstract enough that it almost misses the point)?
That's not really a definition of time, just a way to postulate its direction. Time as a physical unit has been decreed to be the rate of decay of a certain Cesium atom; i.e., a fixed regular interval, whereas the increase of entropy varies from moment to moment. E.g. right now I'm typing and before I wasn't, that doesn't mean time is going ever so slightly faster because of that ...
What you had in mind is the SI-definition of the second, which reads (http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.ht...):
"""
The second is the duration of 9 192 631 770 periods
of the radiation corresponding to the transition
between the two hyperfine levels of the ground state
of the caesium 133 atom.
"""
The cesium particles have not decayed, in principle you could run forever on a certain supply of atoms... even though in practice a Cs-beam is produced on one side, at a hot filament, and dumped to the other side of the clock after passed through the apparatus that performs the steps described above. They will be disposed of when the lifetime of the beam-tube is reached (typically 10 years or so with a few grams of cesium inside).