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'And as I understand that, in a system with total entropy, there's no time.'

I've never heard about that, source? As far as I know time has no connection with entropy.

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Since time is a representation of how fast something changes (or moves) in relation to something else, if no process can happen with total entropy, there's nothing to measure time by, so there's no time. Of course then again you're saying that I got this all wrong and that change can happen without it leading to more entropy.


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If we can't measure it doesn't mean that it doesn't exist. I look at it as an extra dimension, like it is present in Special realtivity, while entropy is just a statistical quantity. I am even not sure if there is a good definition of entropy for quantum system. (There could be, I just don't know, and don't remember reading about it.)

Metric is probably more versed in this subject than me, but it seems to me that if we have fluctuations, time should exist.

In most processes that we observe entropy increases, but I'm cautious about applying the notion of entropy to cosmological processes. We can't be sure if it still valid on that scale. We don't have experimental evidence to be sure about it.