Eternal inflation and a thermodynamic treatment of Einstein's equations
  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. 
Jose Tomas Galvez Ghersi, Ghazal Geshnizjani, Federico Piazza, Sarah   Shandera
gr-qc astro-ph.CO hep-th