I guess I missed the concession. All timekeeping devices use energy in a precise fashion, though to different degrees.
The point is that, whether that is true or not, it isn't relevant. Clocks are about comparing events. What sort of event it is makes no difference.
The used up energy must be renewed for the timepiece to do its job.
But that isn't the reason WHY it makes a good clock. Indeed, if it were possible to make perpetual motion machines, they would totally make the best clocks! If anything it is entropy that forces inaccuracies into clocks.
The hourglass comparison is easier to see than the hyper-fine energy levels in an atomic clock, but it's the same concept, and they both involve "using up energy" (transitioning one form of energy into a less useful form), which is another way of saying entropy.
I agree that is what entropy is but it's beside the point.
Every engine in every car you've ever driven is up to its neck in entropy. Is driving therefore a measure of entropy or isn't just a point of trivia about the way machines work?
In other words, the fact that clocks eventually run down is a statement about the nature of machines in general, not time or the way in which the events that the clock is ticking off are being used.
God Himself is not entropic, is He? Indeed, He is the ultimate source, the very fountainhead of all energy, He is the only "perpetual motion machine" (if you'll forgive demoting God with such terminology) and His actions are events that can be used as a sort of clock. We are in the era of God's first creation. It had a beginning and it will have an end (not because of entropy but because God will end it) and then the new era of God's second creation will begin and we'll be able to measure the duration of that second era in terms of however long the first will have lasted (not that anyone would necessarily want to do that).
You've already agreed to that point. But the atomic clocks help to understand that the entropy concept is the important one, because of the transition to the lower energy level from which the desired frequency of output signal is derived, and that it needs to be repeated, repeatedly.
No. It is not the fact that the event is entropic that matters. Any event will do, entropic or otherwise. Entropy is not a necessary condition for the concepts of time and/or clocks to be utilized.