# Thermodynamics and critical behaviors of topological dS black holes with nonlinear source

## TL;DR

This paper explores the thermodynamic behavior and phase transitions of topological de Sitter black holes influenced by nonlinear electrodynamics, revealing second order phase transitions similar to those in Anti-de Sitter spacetime.

## Contribution

It introduces the effects of nonlinear electrodynamics on the thermodynamics and phase structure of dS black holes, highlighting the role of the nonlinearity parameter and electric charge.

## Key findings

- Black holes exhibit phase transition and criticality similar to AdS black holes.
- Nonlinearity parameter and electric charge influence phase structure.
- Critical phase transition identified as second order.

## Abstract

We discuss black hole solutions of Einstein gravity in presence of nonlinear electrodynamics in dS spacetime. Considering prescribed entropy, thermodynamic volume of dS spacetime, We investigate properties of the effective thermodynamic quantities under influence of nonlinearity parameter $\alpha$. They show a similar phase transition and criticality properties with that of black holes in AdS spacetime. And the nonlinearity parameter $\alpha$ combined with electric charge is found to have effects on the phase structure. By the Ehrenfest equations we prove the critical phase transition is a second order equilibrium transition.