# Thermodynamic interpretation of the de Sitter swampland conjecture

## TL;DR

This paper offers a thermodynamic perspective on the de Sitter swampland conjecture, linking bounds on the potential's derivatives to phase conditions and entropy considerations, suggesting de Sitter space is statistically disfavored.

## Contribution

It provides a novel thermodynamic interpretation of the de Sitter swampland conjecture, connecting phase transitions and entropy maximization to the conjecture's bounds.

## Key findings

- Bound on $m_{Pl}
abla V/V$ corresponds to positive temperature phase condition.
- De Sitter spacetime is in the negative temperature phase and statistically disfavored.
- Justification of the bound on $m_{Pl}^2
abla^2 V/V$ through potential concavity.

## Abstract

We interpret the de Sitter swampland conjecture in the thermodynamic point of view. When the number of degrees of freedom is enhanced as the modulus rolls down the potential, the bound on $m_{\rm Pl} \nabla V/V$ is equivalent to the condition for the positive temperature phase. The boundary between the positive- and the negative temperature phases is preferred by the classical system since the entropy density is maximized. The distance conjecture imposes that (quasi-)de Sitter spacetime is entirely in the negative temperature phase and statistically disfavored. By investigating the concave potential, we also justify the bound on $m_{\rm Pl}^2 \nabla^2 V/V$.