What is the Entropy in Entropic Gravity?

TL;DR

This paper explores two approaches to deriving gravity from entropy principles—holographic and thermodynamic—highlighting their assumptions, challenges, and implications for understanding gravity's connection to quantum entanglement.

Contribution

It clarifies the assumptions behind holographic gravity and identifies difficulties in defining entropy consistently in thermodynamic gravity, advancing the understanding of gravity-entanglement links.

Findings

Holographic gravity assumptions are partly justified by quantum field theory results.

Thermodynamic gravity faces challenges in defining a consistent entropy.

The study guides future research on gravity's entanglement origins.

Abstract

We investigate theories in which gravity arises as a consequence of entropy. We distinguish between two approaches to this idea: holographic gravity, in which Einstein's equation arises from keeping entropy stationary in equilibrium under variations of the geometry and quantum state of a small region, and thermodynamic gravity, in which Einstein's equation emerges as a local equation of state from constraints on the area of a dynamical lightsheet in a fixed spacetime background. Examining holographic gravity, we argue that its underlying assumptions can be justified in part using recent results on the form of the modular energy in quantum field theory. For thermodynamic gravity, on the other hand, we find that it is difficult to formulate a self-consistent definition of the entropy, which represents an obstacle for this approach. This investigation points the way forward in understanding the connections between gravity and entanglement.