Quantum gravitational effects on statistical mechanics

Abstract

Nowadays, the development of a consistent theory of quantum gravity (QG) continues to be one of the biggest challenges in physics, which has resulted in a number of potential candidates that have not been tested yet. However, phenomenology has joined this task in search of manifestations of the quantum effects of space-time. In particular, the generalized uncertainty principle (GUP) modifies the uncertainty relation between momentum and position, making room for a minimal length, as predicted by candidate theories of QG.

Inspired by the GUP, we derive Planck's distribution by considering a new quantization of the electromagnetic field. We elaborate on the thermodynamics of the blackbody resulting from Wien's law and the Stefan-Boltzmann law. We demonstrate that such thermodynamic laws are modified by the presence of a minimal length. Furthermore, we consider a momentum scale in classical statistical mechanics to see its potential effects in the construction of the microcanonical ensemble.