A series of questions about time and energy.

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For time to not exist, it seems like the energy in a system must be entirely uniform (spatially). Perhaps these things correlate? That is, time and the dispersion (or diffusion) of energy in a system go along with one thing rather than are the same thing. Let’s say we were to have a box in which energy was entirely uniform. Surely, nothing would happen. Everything would be in its ground state. So, there is no way to differentiate between any two moments. But, does that mean time does not exist in that box? Humans will never be able to experience the stoppage of time because their energy is not uniform. Does uniformity of energy require the uniformity of mass? Are the two interchangeable?