Inertial force, Hawking Temperature and Quantum Statistics

TL;DR

This paper investigates the connection between entropic forces, Hawking temperature, and quantum statistics, showing that under certain conditions, the thermodynamic force aligns with inertial force in Schwarzschild spacetime, suggesting quantum effects influence gravity.

Contribution

It introduces a thermodynamic process for states at Hawking temperature and demonstrates the match between entropic and inertial forces, highlighting quantum statistical effects in gravity.

Findings

Thermodynamic force matches inertial force when Bekenstein bound is saturated.

Quantum statistics can produce observable effects in gravity for static observers.

Supports the entropic gravity hypothesis through detailed calculations.

Abstract

To explore the mechanism for the entropic force proposal in Entropic Gravity, we propose a specific thermodynamic process for states thermalized in local Hawking Temperature. We find when Casini's version of the Bekenstein bound is saturated, the thermodynamic force derived in the entanglement first law matches the local inertial force for the Schwarzschild solution, except for a negligible statistics-dependent factor. We argue the gravity viewed by static observers may have observable effects emerged from quantum statistics. The successful detailed calculation in this simple model inspires and is in support of the further development in our following research arXiv:2004.14059.