# S3. Holographic and other cosmologically relevant entropies

Special Session organized by P. Jizba and G. Lambiase

The fundamental connection between gravitation and thermodynamics has been suggested by the discovery of black hole thermodynamics with the Bekenstein-Hawking entropy and Hawking temperature serving as conjugate thermodynamic variables. This conjecture was bolstered 20 years later by Jacobson’s finding that there is a deep relation between gravity and thermodynamics, with the possibility to derive the Einstein field equations from the first law of thermodynamics. The important upshot of this approach was that one can infer the cosmological equations (the Friedmann equations) by combing the first and second law of thermodynamics on the apparent horizon. Entropy appears also in the density of states formula in various holographic scenarios including the string-inspired AdS/CFT correspondence. Important new connection between entropy and gravity was proposed in 2011 by Verlinde in his entropic gravity paradigm, which introduced a novel argument for emergent gravity, based on the holographic principle of ‘t Hooft and Susskind. These results suggest that gravity may be explained as an emergent phenomenon and might possess a thermodynamic or entropic origin.

In recent years, there has been an upsurge of interest in extending these lines of thought to cases where more general entropies are employed. These models account for various modifications of Bekenstein-Hawking’s entropy and/or horizon entanglement entropy. For instance, in the context of loop quantum gravity or entropic cosmology, the area law gets logarithmic corrections due to entanglement of quantum fields inside and outside the horizon. Similarly, the generalized non-additive entropies often lead to more generic power-law instead of area-law behavior. As examples may serve Tsallis’ S_{q,δ} entropy, Barrow entropy, Sharma-Mittal entropy or loop-quantum gravity-inspired Barbero-Immirzi entropy.

It is strongly expected that new physical understanding of the role of entropy in the passage from thermodynamics to gravity should provide novel ingredients and insights on modern cosmology and, in particular, on such pressing issues as dark matter and dark energy. Besides, in the context of holography, such as AdS/QCD and AdS/CMT correspondences this might provide an exciting paradigm in a range of fields from quantum information theory to analog gravity.

The goal of this section is to gather researchers from statistical physics and cosmology communities in order to re-examine the role of holographic and other cosmologically relevant entropies. In this section we have two principal aims in mind:

a) discuss both proper thermodynamic and information-theoretic settings for such entropies

b) focus on entropy-driven gravities and ensuing applications in current cosmology and astrophysics.

A non-exclusive list of topics of interest includes:

- Verlinde entropic gravity and its generalizations

- Tsallis S_{q,δ} entropy and Tsallis cosmology

- Dark matter and dark energy issues in entropy-induced gravity

- Evolution of generalized holographic entropies and Page-like behavior

- AdS/CFT, Kerr/CFT, AdS/QCD, and AdS/CMT entropies and their implications (e.g. Sachdev-Ye-Kitaev model, Bousso entropy bound, etc.)