The entropy of dynamical de Sitter horizons

Recently Hollands, Wald and Zhang proposed a new formula for the entropy of a dynamical black hole. We lift this construction to the dynamical cosmological event horizon of an asymptotically de Sitter spacetime. By introducing a nontrivial correction term in the formula for the entropy, we generalize Gibbons and Hawking’s “first law of event horizons” to non-stationary eras. We also develop the non-stationary physical process first law between two arbitrary horizon cross-sections for the cosmological event horizon.