Abstract:
There is a deep link between gravity and thermodynamics; in a precise way gravity can be derived from entanglement entropy in conformal field theories. However this depends crucially on properties of horizons, and asymptotic symmetries of phase space. 

To explore how this relation behaves under dynamical processes, we consider covariant phase space enhanced with bulk symmetries. As is well known (but will be gently described), the Noether-Wald entropy has an explicit form in terms of the Abbott-Deser-Tekin conserved surface charges of gauge theories. We discuss a new vector contribution to the Abbott-Deser-Tekin charges, as well as to the central charge. 

In applying this to the causal diamond in (A)dS, we derive a relation, based on the conformal invariance of horizons, that allows us to find slices where the zeroth law holds, as well as the degree to which a first law arises on the phase space.

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