To the construction of the thermodynamics of quantum nonextensive systems in the framework of the statistics of Tsallis

Within the framework of quantum statistics of Tsallis, based on parametric non-additive entropy associated with the density matrix, thermodynamic equations for a large canonical quantum-mechanical ensemble are obtained. A generalization of the zero law of thermodynamics for independent quantum systems at their thermal contact is obtained, which introduces the so-called physical temperature different from the inversion of Lagrange multiplier $\beta$. Taking into account the generalized first law of thermodynamics and Legendre transformation, the modified thermodynamic relations in Tsallis statistics are considered. The second law of thermodynamics is discussed on the basis of the convexity property of Ratier–Kannappan discrimination information generalized to the quantum case. Spontaneous transitions between stationary states of a complex quantum-mechanical system are studied and Boltzmann's $H$-theorem is proved.
The developed approach involves the use of nonextensive quantum thermodynamics in various contexts, in particular, concerning the simulation of quantum thermal effects in nanoelectronic devices, in materials science, biomedicine and other quantum technologies.