Thermodynamic partition function from quantum theory for black hole horizons in loop quantum gravity

Abstract: We establish the link between the thermodynamics and the quantum theory of black hole horizons through the construction of the thermodynamic partition function, partly based on some physically plausible arguments, by beginning from the description of quantum states of the horizon, considering loop quantum gravity(LQG) as the underlying theory. Although, the effective `thermalized\rq{} form of the partition function has been previously used in the literature to study the effect of thermal fluctuations of the black hole horizon, nonetheless the direct link to any existing quantum theory (which is here taken to be LQG), especially a derivation of the partition function from the quantum states of the horizon, appears to be hitherto absent. This work is an attempt to bridge this small, but essential, gap that appears to be present between the existing literature of quantum theory and thermodynamics of black holes. Further, it may be emphasized that this work is {\it only} concerned with the {\it metric independent} approaches to black hole thermodynamics.