Stationary entropies after a quench from excited states in the Ising chain

We consider the asymptotic state after a sudden quench of the magnetic field in the transverse field quantum Ising chain starting from excited states of the pre-quench Hamiltonian. We compute the thermodynamic entropies of the generalised Gibbs and the diagonal ensembles and we find that the generalised Gibbs entropy is always twice the diagonal one. We show that particular care should be taken in extracting the thermodynamic limit since different averages of equivalent microstates give different results for the entropies