## Life, the Universe, and Everything: Entropy

Posted in cosmology with tags , on October 5, 2009 by Grad Student

Here’s the abstract of a curious paper by Egan and Lineweaver I saw on astro-ph a while back:

Using recent measurements of the supermassive black hole mass function we find that supermassive black holes are the largest contributor to the entropy of the observable Universe, contributing at least an order of magnitude more entropy than previously estimated. The total entropy of the observable Universe is correspondingly higher, and is $S_{obs} = 3.1^{+3.0}_{-1.7}\xt{104} k$. We calculate the entropy of the current cosmic event horizon to be $S_{CEH} = 2.6 \pm 0.3 \xt{122} k$, dwarfing the entropy of its interior, $S_{CEH int} = 1.2^{+1.1}_{-0.7}\xt{103} k$. We make the first tentative estimate of the entropy of dark matter within the observable Universe, $S_{dm} = 10^{88\pm1} k$. We highlight several caveats pertaining to these estimates and make recommendations for future work.

It is cool to think that black holes are the dominate contributors of entropy in the universe, but why is this important for understanding the universe?  Here’s the opening line of the paper:

The entropy budget of the Universe is important because
its increase is associated with all irreversible processes, on
all scales, across all facets of nature: gravitational clustering,
accretion disks, supernovae, stellar fusion, terrestrial
weather, chemical, geological and biological processes

The entropy budget of the Universe is important because its increase is associated with all irreversible processes, on all scales, across all facets of nature: gravitational clustering, accretion disks, supernovae, stellar fusion, terrestrial weather, chemical, geological and biological processes.

Okay, we know this, any other reasons?

That the increase of entropy has not yet been capped by some limiting value, such as the holographic bound (’t Hooft 1993; Susskind 1995) at Smax  10123k (Frampton et al. 2008), is the reason dissipative processes are ongoing and that life can exist.

Mmmm, it appears that that’s it.  I can’t quite grasp why this estimate of the universe’s entropy helps us understand the universe better.  Perhaps it is important for understanding why the universe started out in such a low entropy state (cosmologists like Sean Carroll and Roger Penrose like to think about these things).