Role of Quantum Entropy and Establishment of H-Theorems in the Presence of Graviton Sinks for Manifestly-Covariant Quantum Gravity

• Main Authors: Massimo Tessarotto, Claudio Cremaschini
• Format: Article
• Language: English
• Published: MDPI AG 2019-04-01
• Series: Entropy
• Subjects: covariant quantum gravity; Gaussian solutions; Boltzmann–Shannon entropy; H-theorem
• Online Access: https://www.mdpi.com/1099-4300/21/4/418

Based on the introduction of a suitable quantum functional, identified here with the Boltzmann–Shannon entropy, entropic properties of the quantum gravitational field are investigated in the framework of manifestly-covariant quantum gravity theory. In particular, focus is given to gravitational quantum states in a background de Sitter space-time, with the addition of possible quantum non-unitarity effects modeled in terms of an effective quantum graviton sink localized near the de Sitter event horizon. The theory of manifestly-covariant quantum gravity developed accordingly is shown to retain its emergent-gravity features, which are recovered when the generalized-Lagrangian-path formalism is adopted, yielding a stochastic trajectory-based representation of the quantum wave equation. This permits the analytic determination of the quantum probability density function associated with the quantum gravity state, represented in terms of a generally dynamically-evolving shifted Gaussian function. As an application, the study of the entropic properties of quantum gravity is developed and the conditions for the existence of a local H-theorem or, alternatively, of a constant H-theorem are established.