Thermodynamic and quantum fluctuations of horizon area

TL;DR

The paper investigates how quantum and thermodynamic fluctuations relate in systems with event horizons. It analyzes quantum area fluctuations of black holes via canonical variables $A$ and $K=1/(4G)$, thermodynamic fluctuations of the de Sitter horizon, and a Planckon-based non-extensive toy model to illustrate entropy variance. A central result is the area variance $⟨(ΔA)^2⟩ = 4 G ħ ⟨A⟩$, with the de Sitter entropy obeying $S(V_H)=A/(4Għ)$, linking bulk thermodynamics to horizon properties; the Planckon ensemble reveals non-extensive entropy accumulation while recovering conventional Poisson fluctuations in the extensive limit. Overall, the work highlights a deep interplay between quantum gravity and horizon thermodynamics, suggesting gravity as a bridge between quantum and thermal fluctuations and touching on possible horizon-entropy quantization.

Abstract

The event horizon is a source of irreversibility, analogous to statistical irreversibility. This is why for systems with an event horizon there is no difference between quantum and thermal fluctuations. Quantum processes of quantum tunneling determine the thermodynamics of these systems, their temperatures, entropies and fluctuations. We considered three examples of entropy variance that support this point of view: (i) the variance of the area of the black hole horizon, obtained by consideration of quantum fluctuations; (ii) the variance of the entropy of the Hubble volume in the de Sitter state, obtained by consideration of thermal fluctuations; and (iii) the variance of entropy in integers in the Planckon model, determined by the Poisson distribution.