Super-statistics and quantum entanglement in the isotropic spin-1/2 XX dimmer from a non-additive thermodynamics perspective

TL;DR

This paper investigates how temperature fluctuations modeled by super-statistics affect quantum entanglement in a spin-1/2 XX model, revealing the importance of proper energy constraints for accurate thermodynamic and entanglement analysis.

Contribution

It introduces a non-additive thermodynamics approach using super-statistics with specific energy constraints to analyze entanglement in out-of-equilibrium quantum systems.

Findings

Temperature fluctuations influence entanglement measures.

Proper energy constraints are crucial for accurate thermodynamic descriptions.

Analytical expressions for entanglement are derived under non-additive thermodynamics.

Abstract

In this paper, the impact of temperature fluctuations in the entanglement of two qubits described by a spin-1/2 XX model is studied. To describe 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 the case when the Tsallis restrictions are not imposed on the density operator.