Thermodynamics of Quantum Isolated Horizons with model Hamiltonians

TL;DR

This paper develops a comprehensive thermodynamic framework for Quantum Isolated Horizons using a general model Hamiltonian, deriving the energy spectrum and analyzing equilibrium properties.

Contribution

It introduces a general Hamiltonian structure for QIHs and derives their thermodynamic behavior, connecting quantum models with classical limits.

Findings

Derived the energy spectrum of QIHs from the model Hamiltonian.

Established the thermodynamic properties of QIHs in the canonical ensemble.

Connected quantum results with classical equilibrium temperature.

Abstract

Following a recent proposal, we consider the most general structure possible for the Hamiltonian operator associated with the Quantum Isolated Horizon(QIH) with explanations of the underlying physical motivations. An extensive thermodynamic analysis with this model Hamiltonian is presented. Considering {\it fixed} number of punctures, the canonical partition function can now be written in the usual energy ensemble. Arguing that the known classical results must follow in the correspondence limit (viz. the equilibrium temperature as observed by a local observer) the model is fixed, yielding the energy spectrum of the QIH.