# Partition function for a volume of space

### APA

Jacobson, T. (2023). Partition function for a volume of space. Perimeter Institute. https://pirsa.org/23010068

### MLA

Jacobson, Ted. Partition function for a volume of space. Perimeter Institute, Jan. 12, 2023, https://pirsa.org/23010068

### BibTex

@misc{ pirsa_23010068, doi = {10.48660/23010068}, url = {https://pirsa.org/23010068}, author = {Jacobson, Ted}, keywords = {Quantum Gravity}, language = {en}, title = {Partition function for a volume of space}, publisher = {Perimeter Institute}, year = {2023}, month = {jan}, note = {PIRSA:23010068 see, \url{https://pirsa.org}} }

Ted Jacobson University of Maryland, College Park

## Abstract

In their seminal 1977 paper, Gibbons and Hawking (GH) audaciously applied concepts of quantum statistical mechanics to ensembles containing black holes, finding that a semiclassical saddle point approximation to the partition function recovers the laws of black hole thermodynamics. In the same paper they insouciantly applied the formalism to the case of boundary-less de Sitter space (dS), obtaining the expected temperature and entropy of the static patch. To what ensemble does the dS partition function apply? And why does the entropy of the dS static patch decrease upon addition of Killing energy? I’ll answer these questions, and then generalize the GH method to find the approximate partition function of a ball of space at any fixed proper volume. The result is the exponential of the Bekenstein-Hawking entropy of its boundary.

Zoom link: https://pitp.zoom.us/j/91961890091?pwd=R3lZWHNIQUUzSldzS3kyclJKR3JXdz09