Super-statistics and quantum entanglement in the isotropic Heisenberg $XY$ model from a non-additive thermodynamics perspective.

In this paper, the impact of temperature fluctuations in the entanglement of two qubits described by the Heisenberg $XY$ model is studied. To model the out-of-equilibrium situation, super-statistics is used with fluctuations given by a $\chi^2$ distribution function, and its free parameters are chosen in such a way that resembles the non-additive Tsallis thermodynamics. In order to preserve the Legendre structure of the thermal functions, particular energy constraints are imposed on the density operator and the internal energy. Analytical results are obtained using an additional set of constraints after a parametrization of the physical temperature. We show that the well-known parametrization may lead to undesirable values of the physical temperature so that by analyzing the entropy as a function of energy, the correct values are found. The quantum entanglement is obtained from the Concurrence and is compared with when the non-additive prescription is not imposed.