The closest answer to this I can think of is to do with entropy. This won’t be so much “time”, but no thermodynamic free energy. This is called “Heat Death of the Universe”, but it’s not necessarily just about things getting cold. It’s essentially like all the processes winding down. Time will still go on, but nothing much will be happening.
This is a brilliant question! Kerrianne answered it pretty nicely, but I had one thing to add – if you like thinking about his, consider reading the short story “The Last Question” by Isaac Asimov. It’s basically about the universe eventually running out – something that seems impossibly far away to us, but will eventually happen!
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