A physical axiom is advanced that relates to the density of neutrons and their individual contribution to the operationally determinable behavior of a reactor. The variational principle derived from this axiom is of a general form applicable to systems in which the time dependency of the coefficients of the equations prevents a separation into conventional eigenfunctions and eigenvalues. The physical significance of the independent variation of two field functions is investigated. The treatment of the nonseparable systems and the variational principle to which we are led are both independent of any particular physical model employed to represent the system and appear to be applicable to a variety of nonconservative, continuous, and time-dependent systems in mathematical physics. The more well-known properties of the separable problem are derived from the principle as “the exception proving the rule” in an attempt to associate physical meaning with the commonly employed forms. Thus a discussion is given of the relation of the Green's function to both fields and the Joint Error is introduced as a criterion for the completeness of biorthogonal sets. Although the variational principle derived is not applicable to variation of the coefficients of the equations through nonlinearities, it is indicated how the present approach may be extended to account for nonlinearities.