Time is distance measured in inertial matter divided by the speed of light. It is a relationship between inertial and non-inertial matter.
Time is not entropy for the simple reason that entropy does not exist in a perfect closed system, and the universe is such a system.
Entropy is the phenomenon of spent energy that cannot be reused. Entropy is burned paper that cannot be made into paper again. Entropy is burned oil that cannot be made into fuel again.
However, burned paper can be made into paper again and burned fuel can be made into fuel again. Nature does this all the time. It's called photosynthesis.
And the energy used to produce the paper and fuel is exactly the same as the energy gained by burning this. There is no loss. The heat that dissipates into space is lost to us here on Earth, but it is not lost to the universe.
Entropy is merely an expression of our limited ability to do the second half of the great energy cycle. We burn stuff, and things that we make rust and fall apart. We are incapable of putting Humpty Dumpty together again. However, nature produces new eggs all the time. In the great scheme of things, there is no entropy.
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