Thermodynamic and Superstatistical Analysis of a Harmonic Oscillator with Position-Dependent Mass

Abstract

In this paper, we investigate the thermodynamic behavior of a quantum harmonic oscillator with a positiondependent mass (PDM), where spatial inhomogeneity is introduced through a deformation parameter α. Using the exact energy spectrum, we derive the associated thermodynamic quantities and perform a superstatistical analysis by incorporating fluctuations of the inverse temperature. Within this framework, we examine how mass deformation affects the superstatistical energy distribution and the resulting modified thermodynamic responses. Our results show that increasing α leads to a reduction in entropy and specific heat, reflecting a confinementinduced decrease in the number of accessible microstates. The partition function and free energy display smooth variations across all parameter regimes, indicating the absence of critical phase transitions. Overall, this work highlights the combined effects of mass deformation and superstatistical fluctuations on the thermal behavior of the system and reveals distinctive features that differentiate the PDM oscillator from its constant-mass counterpart.