  We prove that throughout the satisfiable phase, the logarithm of the number
of satisfying assignments of a random 2-SAT formula satisfies a central limit
theorem. This implies that the log of the number of satisfying assignments
exhibits fluctuations of order $\sqrt n$, with $n$ the number of variables. The
formula for the variance can be evaluated effectively. By contrast, for
numerous other random constraint satisfaction problems the typical fluctuations
of the logarithm of the number of solutions are {\em bounded} throughout all or
most of the satisfiable regime.
