An exact derivation of nonlinear, nonequilibrium thermodynamics proposed by Robertson, effected by operating with a non-Hermitian (P) over cap(R) on the Liouville equation, is applied to give an exact statistical derivation of extended thermodynamics. This includes variables that are even under time reversal and others that are their time derivatives. Entropy is given by the Jaynesian information-theoretic model. if the phenomenological coefficients are expanded in powers of thermodynamic forces, antireciprocal relations hold to all orders. Symmetric reciprocity holds exactly in linear approximation and, in the nonlinear regime, for very short times where it may apply to relaxation of fast variables, approximately. The formalism does not readily provide expressions for long-time limits and steady-state transport coefficients. One obtains exact expressions for fluxes of measurable variables as functionals of all the measurable variables. Thus addition of a hierarchy of fluxes as internal variables is incompatible with an information-theoretic entropy.