Generalized Gravitational Entropy from Total Derivative Action

TL;DR

This paper demonstrates that total derivative terms in gravitational action do not contribute to generalized gravitational entropy, ensuring consistency with holographic entanglement entropy and thermodynamic laws.

Contribution

It shows that total derivative terms in the gravitational action yield zero generalized entropy, clarifying their role in holographic and field-theoretic entanglement entropy calculations.

Findings

Total derivatives produce zero generalized gravitational entropy.

Nonzero entropy from total derivatives would break holographic and field-theoretic entropy match.

Non-vanishing total derivative entropy could violate the second law of thermodynamics.

Abstract

We investigate the generalized gravitational entropy from total derivative terms in the gravitational action. Following the method of Lewkowycz and Maldacena, we find that the generalized gravitational entropy from total derivatives vanishes. We compare our results with the work of Astaneh, Patrushev, and Solodukhin. We find that if total derivatives produced nonzero entropy, the holographic and the field-theoretic universal terms of entanglement entropy would not match. Furthermore, the second law of thermodynamics could be violated if the entropy of total derivatives did not vanish.