The Minimal Length and the Quantum Partition Functions

TL;DR

This paper investigates how a minimal length, derived from the Generalized Uncertainty Principle, affects the thermodynamics of physical systems by analytically calculating modified quantum partition functions and thermodynamic quantities.

Contribution

It introduces a general analytical scheme to compute quantum partition functions under minimal length deformations and compares results with classical thermodynamics.

Findings

Modified internal energy and heat capacity in the anti-Snyder framework

Analytical expressions for partition functions with minimal length effects

Comparison between deformed and classical thermodynamic results

Abstract

We study the thermodynamics of various physical systems in the framework of the Generalized Uncertainty Principle that implies a minimal length uncertainty proportional to the Planck length. We present a general scheme to analytically calculate the quantum partition function of the physical systems to first order of the deformation parameter based on the behavior of the modified energy spectrum and compare our results with the classical approach. Also, we find the modified internal energy and heat capacity of the systems for the anti-Snyder framework.