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

Abstract

Recently, Barrow proposed a modified area–entropy relation S=(A/A0)1+Δ/2, where the exponent Δ, ranges 0≤Δ≤1, by taking account of the quantum gravitational deformation effects to the black hole’s surface. In recent literature, this horizon entropy has been adopted to the cosmological context. Following this, we obtained the law of emergence, which describes the dynamics of the universe, with Barrow entropy in the context of equilibrium thermodynamics (unified first law and Clausius relation). However, when considering Barrow entropy (a non-Bekenstein entropy), an additional entropy generation arises owing to the non-equilibrium thermodynamics. The corresponding field equation bears an effective coupling strength, which connects the geometry with an effective energy–momentum tensor. We derived the law of emergence by using the non-equilibrium description of the thermodynamic principle, which accounts for the addition entropy production term. We compared it with that of the equilibrium description. In addition, we checked the consistency of the modified law in the context of entropy maximization. Interestingly, we found that the non-equilibrium entropy generation rate decreases gradually, and the universe evolves to an equilibrium state of maximum entropy corresponding to the de Sitter epoch.