The Einstein-Hilbert Action Horizons and Connections with Thermodynamics

TL;DR

This paper explores how the Einstein-Hilbert action relates to thermodynamics by deriving it through free energy minimization on black hole horizons, suggesting a deep connection between gravity and thermodynamic principles.

Contribution

It introduces a novel perspective by deriving the Einstein-Hilbert action via free energy minimization on black hole horizons, linking gravity to thermodynamics.

Findings

The Einstein-Hilbert action can be obtained by minimizing free energy.

Horizon entropy plays a key role in this derivation.

Potential generalizations to other physical systems are discussed.

Abstract

It is shown that the Einstein-Hilbert action can be constructed by minimizing free energy. The entropy used to determine the free energy is determined on the horizon of a black hole. Some further considerations with regard to generalizations of these ideas to other situations of physical importance are presented as well.