Bulk entropy is crucial to validate the second law of the extended black hole thermodynamics

TL;DR

This paper emphasizes the importance of bulk entropy in extended black hole thermodynamics, showing that accounting for matter/energy entropy during vacuum transitions is essential to uphold the second law.

Contribution

It introduces the role of bulk entropy in validating the second law within extended black hole thermodynamics during vacuum decay processes.

Findings

Bulk entropy is crucial for the second law validation.

Ignoring bulk entropy can lead to entropy decrease scenarios.

Environmental effects influence holographic interpretations.

Abstract

The extended black hole thermodynamics in which the cosmological constant plays the role of pressure significantly enriches the phase structure of the theory. In order to understand the extended black hole thermodynamics more precisely, we let the value of the cosmological constant vary dynamically via tunneling from one vacuum to another in a black hole induced vacuum decay. In this process, entropy of the matter/energy released by a black hole is crucial to validate the second law of thermodynamics. In other words, without taking this bulk entropy into account, entropy associated with the black hole and cosmological horizons may not always increase. Since the bulk entropy is not represented by the black hole and the cosmological horizons, this result calls for a more careful interpretation of the holographic principle in which environmental effects are taken into account.