Majorization relations and disorder in generalized statistics

The theory of majorization is applied to examine the disorder properties of generalized thermal distributions arising in non-extensive statistics. We show that they share with the Boltzmann-Gibbs thermal state the property of becoming more mixed as the temperature increases, implying the increase of any associated disorder measure. We also show that power-law distributions exhibit a second mixing parameter associated with the non-extensivity index. As application, we examine the thermal response of quantum entanglement in a spin system for different statistics.