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shrinking universe

Anyone know this story?

I've been trying to find two short stories that I read years ago, so far with little success. AFAIR they were both in paperback anthologies published around the mid-1960s:

1. The first is set in the world as we know it, but someone discovers that our universe is shrinking. No one noticies anything because of course everything is shrinking at the same pace - except the speed of light, so by the end of the story everything takes on a red-shift and eventually vanishes altogether.

Ask The Cloud: What is life like in a shrinking universe?

I'm contemplating some ideas for a story at the moment, one of the topics that comes up, is what life would be like in a shrinking (rather than expanding) universe.

Would entropy be always decreasing? What would that mean? What would it be like to live in such a universe? What sort of things would be different? Would life arise? Would it be more or less the same?

I'd love to hear your ideas