Application of constrained forms of the Tsallis entropy in thermodynamic properties of graphene based on modified Heisenberg model

This study introduces a non-relativistic theoretical model constructed through a modified Heisenberg algebra, where the momentum commutator is defined in terms of pseudo-spin. Using this framework, the study derives the low-energy electronic excitations in graphene. The Landau quantization is then examined by applying a perpendicular uniform magnetic field to the graphene sheet. To explore the system’s thermodynamic properties, constrained Tsallis entropy formulations are utilized, enabling a detailed investigation of key thermodynamic quantities such as entropy and specific heat. The Tsallis non-extensive statistical approach is applied to determine the probability distribution and partition function for both positive and negative energy states. From this formalism, key magnetic and thermodynamic features are extracted. Notably, the magnetic susceptibility is found to be consistently positive, suggesting a paramagnetic behavior in all energy regimes. Additionally, the specific heat demonstrates a peak-like profile, with the temperature at which this peak occurs, being influenced by the non-extensive parameter. These findings underscore the utility of Tsallis statistics in characterizing the constrained quantum dynamics of graphene.