Thermodynamic and quantum fluctuations of horizon area

TL;DR

This paper explores the connection between quantum and thermal fluctuations of horizon areas, demonstrating that quantum tunneling processes govern the thermodynamics of systems with event horizons through three illustrative examples.

Contribution

It shows that quantum and thermal fluctuations of horizon areas are fundamentally linked, supported by three different models and calculations.

Findings

Quantum fluctuations determine black hole horizon area variance.

Thermal fluctuations influence entropy variance in de Sitter space.

Poisson distribution describes entropy variance in the Planckon model.

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.