Entanglement in a superstatistical system

Many complex systems exhibiting fluctuations can be described by decomposing their dynamics at different scales. Their statistical properties are then given by a mixture of statistics, i.e., superstatistics. In this paper, we study quantum entanglement in a system, obeying a superstatistical model. Such an approach is expected to be a suitable approximation for a continuously varying temperature field that has a temporal correlation length, much larger than the relaxation time. We consider a Heisenberg chain, subject to temperature fluctuations, and its extension in presence of the Dzyaloshinskii-Moriya anisotropic antisymmetric interaction, and explore the effect of different superstatistics (χ2, Log-normal, and F distributions) on entanglement. It is shown that temperature fluctuations can prevent entanglement from vanishing at larger temperatures than predicted for the same system at thermal equilibrium.