Emergence of cosmic space and horizon entropy maximization from Tsallis and Cirto entropy

Abstract

In this note by use of the idea of the emergence of cosmic space suggested by Padmanabhan (Emergence and expansion of cosmic space as due to the quest for holographic equipartition; Res Astro Astrophys 12:891, 2012), we derive the modified Friedmann equation of a Friedmann-Robertson-Walker (FRW) Universe from Tsallis and Cirto entropy in $$(n+1)$$ ( n + 1 ) dimension with any spatial curvature. We investigate further the consistency of the law of emergence with the maximization of horizon entropy in the context of Tsallis and Cirto horizon entropy. Our results reveal the deep connection between the law of emergence and horizon thermodynamics.

From the emergence of cosmic space to horizon thermodynamics in Barrow entropy-based Cosmology

“…As a result, we have shown that both arguments lead to the same constraint, thus allowing to interpret the law of emergence as a tendency of our Universe to extremize horizon entropy. It is worth mentioning that this outcome fits with results formerly obtained in Einstein, Gauss-Bonnet and Lovelock gravities [25,26] and in the context of non-extensive Tsallis entropy [21]. In this sense, our work provides an effort toward the extension of the gravity-thermodynamic connection to a quantum gravity-like scenario.…”

“…Similarly to [21], the definition (13) of number of surface degrees of freedom becomes 3 and ( 23) are correctly dimensionless for any value of n and . On the other hand, it is not clear how the corresponding definitions in [21] can be such for Tsallis pa-…”

“…is a constant that plays the same role as γ in the definition (37) of [21]. Notice that c → 1 for n = 3, so that Eq.…”

“…Recently, Eq. ( 1) has also been applied to BIonic systems [16], brane scenarios [17][18][19] and minimal length frameworks [20] (see [21] and references therein for more studies on the subject).…”

Emergence of cosmic space in Tsallis modified gravity from equilibrium and non-equilibrium thermodynamic perspective

“…Further, the author obtained the Friedmann equations from a newly proposed modified law of emergence. Later, this was extended to (n + 1)-dimensional non-flat FRW universe by Chen [61]. Recently, Basari et al [49] obtained the law of emergence through a unified expansion law derived from the equilibrium first law of thermodynamics, for the Tsallis entropy given by…”