Reduced Equations of Motion for Generalized Fluxes and Forces in the Continued-Fraction Expansion

With the aid of Mori's projection operator method, it is shown that the mechanical equations of motion for flux variables can be transformed rigorously into the reduced form da, (t) / dt=iliJr a1 (t)-J: ds [,P1 (t-s) + ¢1 (t-s)] · a1 (s) + g1 (t) + jj(t), where a, (t) is a column matrix of generalized fluxes standing for the j·th order time derivative of the column matrix of state variables a, (t),