Bekenstein bound from the Pauli principle

TL;DR

This paper demonstrates that the Bekenstein bound naturally arises from the Pauli exclusion principle within a fermionic black hole model, linking entanglement, entropy, and thermodynamics through a unified approach.

Contribution

It introduces a fermionic toy model of black hole evaporation showing the Bekenstein bound as a consequence of the Pauli principle and connects various entropies via Thermofield Dynamics.

Findings

Derivation of the Bekenstein bound from fermionic degrees of freedom.

Unified explanation of entanglement, Bekenstein, and thermodynamic entropies.

Observation of a Page-like entropy evolution in the model.

Abstract

Assuming that the degrees of freedom of a black hole are finite in number and of fermionic nature, we naturally obtain, within a second-quantized toy model of the evaporation, that the Bekenstein bound is a consequence of the Pauli exclusion principle for these fundamental degrees of freedom. We show that entanglement, Bekenstein and thermodynamic entropies of the black hole all stem from the same approach, based on the entropy operator whose structure is the one typical of Takahashi and Umezawa's Thermofield Dynamics. We then evaluate the von Neumann black hole--environment entropy and noticeably obtain a Page-like evolution. We finally show that this is a consequence of a duality between our model and a quantum dissipative-like fermionic system.