Thermodynamic of the $f(Q)$ universe

TL;DR

This paper explores the thermodynamics of the $f(Q)$ universe, analyzing horizon thermodynamics, phase transitions, and the effects of trivial and nontrivial connections, revealing quantum gravity corrections and non-equilibrium states.

Contribution

It provides a novel analysis of horizon thermodynamics in $f(Q)$ gravity, including entropy corrections and the thermodynamic implications of nontrivial connections.

Findings

Entropy correction matches loop quantum gravity form

Phase transition critical exponents align with mean field theory

Nontrivial connections imply non-equilibrium thermodynamic states

Abstract

We investigate thermodynamics of apparent horizon in the $f(Q)$ universe with trivial and nontrivial connections. We first explore the perspectives of the first law, generalized second law and $P-V$ phase transition with trivial connection. We show that the lowest-order correction of entropy has the same form as that in loop quantum gravity, and the critical exponents of the phase transition caused by the lowest-order correction are consistent with those in mean field theory. We then examine the thermodynamic implication of nontrivial connections. We find that nontrivial connections in the $f(Q)$ universe imply non-equilibrium states from the perspective of thermodynamics.