  Despite the importance of the Second Law of Thermodynamics, it is not
absolute. Statistical mechanics implies that, given sufficient time, systems
near equilibrium will spontaneously fluctuate into lower-entropy states,
locally reversing the thermodynamic arrow of time. We study the time
development of such fluctuations, especially the very large fluctuations
relevant to cosmology. Under fairly general assumptions, the most likely
history of a fluctuation out of equilibrium is simply the CPT conjugate of the
most likely way a system relaxes back to equilibrium. We use this idea to
elucidate the spacetime structure of various fluctuations in (stable and
metastable) de Sitter space and thermal anti-de Sitter space.
