Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity

Understand

We study the semi-classical thermodynamics of two-dimensional de Sitter space ($\text{dS}_{2}$) in Jackiw-Teitelboim (JT) gravity coupled to conformal matter.

• We extend the quasi-local formalism of Brown and York to $\text{dS}_{2}$, where a timelike boundary is introduced in the static patch to uniquely define conserved charges, including quasi-local energy.
• The boundary divides the static patch into two systems, a cosmological system and a black hole system, the former being unstable under thermal fluctuations while the latter is stable.
• A semi-classical quasi-local first law is derived, where the Gibbons--Hawking entropy is replaced by the generalized entropy.