Currently i am dealing with a QB out of the Heisenberg spin chain, say XX, and for certain particular values of spin-orbit coupling, I am getting negative ergotropy, and the initial state i am assuming for the QB is Gibbs thermal state.

I dont find literature on this issue on how it can be possible, and from the computational point of view, i can safely say the calculations are right, but I can't say anything about the occurrence of negative ergotropy.