The gravity of the situation

On monday night I heard Paul Davies give an interesting public lecture The origin and the end of the Universe in Brisbane. One small aspect that I was particularly interesting was the discussion of the second law of thermodynamics in gravitational systems. He emphasized the following puzzle (in my words).

For an isolated system the entropy can never decrease. In some sense this means that the "order" cannot increase. However, a long time ago matter in the universe was relatively uniform, and now it is not just ordered into galaxies and stars, but even biological life!

The key to resolving this is to realise that in a gravitational system the second law looks different. Uniform "disordered" states do not have low entropy. If you start with a fairly uniform system this is not an equilibrium state. The natural tendency of the system is to evolve to a non-uniform state with clumps of matter. Hence, the "clumpy" state [with a sun which transfers energy to order and sustain biological systems] can actually have the lower entropy.

Clarifying these issues, particularly in a quantitative manner, turns out not to be easy. I found a nice one page article by Mark Buchanan in Nature Physics. It summarises a 2009 paper Gravity, Entropy, and Cosmology: a search for clarity by physics philosopher David Wallace.