Generalized uncertainty principle and thermostatistics: a semiclassical approach

TL;DR

This paper investigates how different generalized uncertainty principles (GUPs) affect thermodynamic properties like internal energy and heat capacity using a semiclassical approach, revealing that these effects depend solely on the algebraic deformation.

Contribution

It provides an exact semiclassical analysis of thermodynamics under two GUP models, highlighting the algebraic dependence of thermodynamic shifts.

Findings

Total shifts depend only on the deformed algebra

Modified internal energy and heat capacity are explicitly calculated

Different GUPs produce distinct thermodynamic modifications

Abstract

We present an exact treatment of the thermodynamics of physical systems in the framework of the generalized uncertainty principle (GUP). Our purpose is to study and compare the consequences of two GUPs that one implies a minimal length while the other predicts a minimal length and a maximal momentum. Using a semiclassical method, we exactly calculate the modified internal energies and heat capacities in the presence of generalized commutation relations. We show that the total shift in these quantities only depends on the deformed algebra not on the system under study. Finally, the modified internal energy for an specific physical system such as ideal gas is obtained in the framework of two different GUPs.