Emergence of cosmic space with Barrow entropy, in non-equilibrium thermodynamic conditions

TL;DR

This paper explores how quantum gravitational effects, modeled by Barrow entropy, influence the emergence of cosmic space in a non-flat universe, highlighting non-equilibrium thermodynamics and entropy maximization.

Contribution

It extends the law of emergence to non-equilibrium conditions using Barrow entropy in a cosmological setting, revealing the universe's approach to equilibrium over time.

Findings

Non-equilibrium behavior is necessary for energy-momentum conservation with Barrow entropy.

Additional entropy production decreases over time, leading to eventual equilibrium.

Entropy maximization constraints are similar in both equilibrium and non-equilibrium cases.

Abstract

Recently, Barrow accounts for the quantum gravitational effects to the black hole surface. Thus the conventional area-entropy relation has modified, $S=(A/A_{0})^{1+\Delta/2},$ with an exponent $\Delta$, ranges $0\le\Delta\le1$, quantifies the amount of quantum gravitational deformation effect to the black hole surface. In recent literature, this horizon entropy has been extended to the cosmological context. Following this, we consider an n+1 dimensional non-flat universe with an apparent horizon as the boundary with appropriate temperature and associated entropy is Barrow entropy. We derived the modified form of the law of emergence from the equilibrium and non-equilibrium thermodynamic principles. Later studied the entropy maximization condition due to the modified law of emergence. On distinguishing the obtained result, it speculates that in order to hold the energy-momentum conservation, the universe with Barrow entropy as the horizon entropy should have non-equilibrium behaviour with an additional entropy production. However, the additional entropy production rate decreases over time, so the system eventually approaches equilibrium. Because of this, the constraint relation for entropy maximization looks similar for both equilibrium and non-equilibrium approaches.