  In pursuing the intriguing resemblance of the Einstein equations to
thermodynamic equations, most sharply seen in systems possessing horizons, we
suggest that eternal inflation of the stochastic type may be a fruitful
phenomenon to explore. We develop a thermodynamic first law for quasi-de Sitter
space, valid on the horizon of a single observer's Hubble patch and explore
consistancy with previous proposals for horizons of various types in dynamic
and static situations. We use this framework to demonstrate that for the local
observer fluctuations of the type necessary for stochastic eternal inflation
fall within the regime where the thermodynamic approach is believed to apply.
This scenario is interesting because of suggestive parallels to black hole
evaporation.
