Infinite Temperature's Not So Hot
Henry Lin, Leonard Susskind
TL;DR
This work addresses the paradox of an infinite Boltzmann temperature for de Sitter horizons by introducing tomperature, a finite temperature-like quantity that governs energy changes and time scales in the infinite-temperature limit. By applying tomperature to the double-scaled SYK (DSSYK) model, the authors show that correlation functions, Hawking-like decay rates, and bulk-horizon correlators acquire finite, thermally interpretable forms consistent with de Sitter physics. The key result is that the tomperature π― remains finite and sets the decay rates and energy costs of horizon quanta, with the holographic parameter π₯ playing the role of the inverse horizon scale, l^{-1}. While DSSYK is a toy model, the findings provide a coherent framework in which de Sitter holography can be described by horizon-local degrees of freedom exhibiting finite tomperature despite an infinite formal temperature. The work thus links entanglement structure, correlation functions, and scrambling in a manner aligned with de Sitter thermodynamics, offering a plausible route toward a holographic description of cosmological horizons.
Abstract
It has been argued that the entanglement spectrum of a static patch of de Sitter space must be flat, or what is equivalent, the temperature parameter in the Boltzmann distribution must be infinite. This seems absurd: quantum fields in de Sitter space have thermal behavior with a finite temperature proportional to the inverse radius of the horizon. The resolution of this puzzle is that the behavior of some quantum systems can be characterized by a temperature-like quantity which remains finite as the temperature goes to infinity. For want of a better term we have called this quantity tomperature. In this paper we will explain how tomperature resolves the puzzle in a proposed toy model of de Sitter holography -- the double-scaled limit of SYK theory.