Equipartition energy, Noether energy and boundary term in gravitational action

TL;DR

This paper clarifies the roles of equipartition and Noether energies in horizon thermodynamics and emergent gravity, showing their relation to boundary terms in the Einstein-Hilbert action and their differences by a factor of two.

Contribution

It elucidates the connection between equipartition and Noether energies and their association with boundary terms in gravitational action, clarifying their roles in horizon thermodynamics.

Findings

E=2TS and E=TS are distinct energies in horizon thermodynamics.

E=TS is related to the Noether charge from the boundary term.

The paper clarifies the contexts where each energy expression applies.

Abstract

In the study of horizon thermodynamics and emergent gravity two natural expressions for energy, E= 2 TS (equipartition energy) and E=TS (Noether energy) arise which differ by a factor 2. I clarify the role of these two expressions in different contexts and show how E=TS is also closely related to the Noether charge arising from the boundary term of the Einstein-Hilbert action.