Thermodynamic Analysis for Harmonic Oscillator with Position-Dependent Mass

TL;DR

This paper investigates how a position-dependent mass affects the thermodynamics of a quantum harmonic oscillator, revealing that increased deformation reduces entropy and specific heat without inducing phase transitions.

Contribution

It provides an exact analysis of thermodynamic properties for a PDM harmonic oscillator, highlighting the impact of spatial inhomogeneity on quantum thermal behavior.

Findings

Increasing deformation parameter {lpha} decreases entropy.

Specific heat diminishes with higher {lpha}.

Partition function remains smooth, indicating no phase transitions.

Abstract

In this paper, we examine the thermodynamic behavior of a quantum harmonic oscillator with a position-dependent mass (PDM), where spatial inhomogeneity is modeled through a deformation parameter {\alpha}. Based on the exact energy spectrum, we explore the resulting thermodynamic quantities and superstatistics. Our findings reveal that increasing {\alpha} leads to a decrease in entropy and specific heat, reflecting a confinement-induced reduction in the number of accessible states. The partition function and free energy exhibit smooth behavior across all parameter regimes, indicating the absence of critical phase transitions. This study underscores the influence of mass deformation on quantum thermal responses and demonstrates that, while the overall thermodynamic trends are consistent with those reported in the literature, certain distinctive features emerge due to the specific form of the deformation.