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Since the universe's entropy is going to increase indefinitely and it is going to be a continuous, does this mean that it will be equal to some power of pi or e or any other transcendental number?

yolo
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1 Answers1

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If by ‘the universe’ you mean everything within our event horizon (a comoving volume), which exists because the expansion of the universe is accelerating due to the vacuum energy density, then the universal entropy growth will asymptote to the entropy of the future cosmic event horizon.

The expansion of the universe will cause comoving objects like galaxies, black holes, photons etc to recede beyond our cosmic event horizon (CEH), taking their entropy with them. However, this is compensated by the CEH entropy, which continues to asymptotically grow toward the de Sitter far future, where there is only vacuum energy.

  • This is all beautifully outlined in this paper by Lineweaver et al A LARGER ESTIMATE OF THE ENTROPY OF THE UNIVERSE.

However, your intuition isn’t wrong, the CEH entropy at the beginning - hot big bang - was a power of pi, see this answer (also implied in Figure 7 of Lineweavers paper)

Mr Anderson
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