Statistical physics in deformed spaces with minimal length

TL;DR

This paper explores how minimal length deformations in space affect thermodynamics, developing a classical approach to compute partition functions that align well with quantum results and reveal reduced degrees of freedom at high temperatures.

Contribution

It introduces a classical method for evaluating partition functions in deformed spaces with minimal length, matching quantum results and highlighting the impact on system degrees of freedom.

Findings

Partition function calculations agree with quantum results.

Minimal length reduces degrees of freedom at high temperatures.

Method applicable to ideal gases and harmonic oscillators.

Abstract

We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat capacity for ideal gas and harmonic oscillators using this method. The obtained results are in good agreement with the exact quantum ones. We also showed that the minimal length introduction reduces degrees of freedom of an arbitrary system in the high temperature limit significantly.