Equipartition energy, Noether energy and boundary term in gravitational action

Abstract

In the study of horizon thermodynamics and emergent gravity two natu-ral expressions for energy, E=2TS(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 howE=TSis also closely related to the Noether charge arising from theboundary termof the Einstein–Hilbert action.