Another link to Sean Carroll's blog: Squelching Boltzmann Brains (And Maybe Eternal Inflation). The discussion of Boltzmann brains has come up many times on LW, starting from this Eliezer's post. Now Sean and his collaborators argue that in an empty expanding universe:

**Quantum fluctuations are not dynamical processes inherent to a system, but instead reflect the statistical nature of measurement outcomes.** Making a denite measurement requires an out-of-equilibrium, low-entropy detection apparatus that interacts with an environment to induce decoherence. Quantum variables are not equivalent to classical stochastic variables. They may behave similarly when measured repeatedly over time, in which case it is sensible to identify the nonzero variance of a quantum-mechanical observable with the physical fluctuations of a classical variable. **In a truly stationary state, however, there are no fluctuations that decohere.** We conclude that systems in such a state|including, in particular, the Hartle-Hawking vacuum never fluctuate into lower-entropy states, including false vacua or congurations with Boltzmann brains.

Although our universe, today or during inflation, is of course not in the vacuum, the cosmic no-hair theorem implies that any patch in an expanding universe with a positive cosmological constant will asymptote to the vacuum. Within QFT in curved spacetime, the Boltzmann brain problem is thus eliminated: a patch in eternal de Sitter can form only a finite (and small) number of brains on its way to the vacuum.

In other words, in an empty universe no macroscopic areas of low entropy can form. And a non-vacuum expanding universe like ours becomes vacuum after a time too short to form more than a few Boltzmann brains.