This paper proposes a GaAs \({/}\) Al0.35Ga0.65As T-shaped quantum wire (QW) under an external magnetic field. The energy eigenvalues and wave function have been determined by the method of expansion of basis sets of the wave functions. The non-extensive Tsallis formalism has been employed. Specific heat and internal energy are calculated for various QW sizes, temperatures and non-extensive parameters ( \(q\) ). The results revealed that the specific heat and internal energy show a peak structure. The number of peaks and the height of the peaks depend on the QW size, temperature and non-extensive parameters. Also, the results show that the specific heat and internal energy at a particular range of temperatures and non-extensive parameters have zero values determined by the cut-off condition in the Tsallis formalism.
