Investigation of Thermodynamic Properties of Classical Oscillators Under Statistical and Superstatistical Frameworks

Abstract

This paper systematically investigates the thermodynamic properties of classical oscillators under different statistical distributions, focusing on the behavior of uniform distribution, two-level distribution, gamma distribution, log-normal distribution, and F-distribution as the nonequilibrium parameter q varies. By calculating Helmholtz free energy and entropy, we reveal the unique patterns and characteristics exhibited by each distribution during the process of moving away from equilibrium. The results show that uniform and two-level distributions exhibit consistent trends of decreasing free energy and increasing entropy under nonequilibrium statistics, reflecting an increase in system disorder. In contrast, the gamma, log-normal, and F-distributions display complex dual-equilibrium point phenomena, where the system can briefly return to equilibrium at specific q values. However, as q further increases, the system rapidly moves away from equilibrium, exhibiting pronounced nonequilibrium characteristics. These findings not only deepen our understanding of nonequilibrium statistical physics but also provide new theoretical perspectives and methods for studying the nonequilibrium behavior of complex systems.