# Schottky Anomaly of deSitter Black Holes

## TL;DR

This paper identifies a Schottky peak in the heat capacity of deSitter black holes, explores quantum models with many spins to explain this behavior, and reviews related particle production phenomena.

## Contribution

It introduces the Schottky anomaly in deSitter black holes and proposes spin-based models to understand their thermodynamics.

## Key findings

- Discovery of a Schottky peak in heat capacity of SdS black holes
- Spin models can partially reproduce black hole thermodynamics
- Connection between Schottky anomaly and particle production in SdS spacetimes

## Abstract

The interplay of black hole and cosmological horizons introduces distinctive thermodynamic behavior for deSitter black holes, including well-known upper bounds for the mass and entropy. We point to a new such feature, a Schottky peak in the heat capacity of Schwarzschild-deSitter (SdS) black holes. With this behavior in mind, we explore statistical models for the underlying quantum degrees of freedom of SdS holes. While a simple two-state spin model gives Schottky behavior, in order to capture the non-equilibrium nature of the SdS system we consider a system with a large number of non-interacting spins. We examine to what extent constrained states of this system reproduce the thermodynamic properties of the black hole. We also review results of a recent study of particle production in SdS spacetimes in light of the Schottky anomaly and our spin models.