A Hamiltonian formulation for two hierarchies of thermodynamic evolution equations

Two hierarchies of thermodynamic evolution equations leading to continued-fraction expansions for generalized frequency- and wavevector-dependent transport coefficients are cast in Hamiltonian form. In the nonlinear regime, the Jacobi identity implies several requirements on the transport coefficients which had not been previously explored and which are beyond the scope of the thermodynamic restrictions coming from the second law.