We analyze the long time limit of the nonequilibrium solutions of a system of multivariable nonlinear kinetic equations with time-dependent rate coefficients, as achieved, for example, by temporal variation of the temperature. If the characteristic time scale attached to the change of rate coefficients is smaller than the relaxation time to equilibrium, then the system is constrained to evolve away, possibly far, from equilibrium. However, after a sufficiently large time the system forgets its past : in the long run all solutions of the kinetic equations tend toward a special (normal) solution which depends on the previous values of the rate coefficients, but it is independent of the initial state of the system. The normal solution may be very different from the equilibrium solution. The occurrence of this type of time-dependent normal regime for the deterministic kinetic equations is intimately connected to a similar behavior of the stochastic evolution equation of the system. In the long run all solutions of the stochastic equation for the state probability also tend toward a normal form which is independent of the initial preparation of the system. The logarithm of the normal form of the state probability is a Lyapunov function of the system of deterministic kinetic equations and plays the role of a generalized thermodynamic potential which may be used for developing a thermodynamic description of the chemical process, A Gibbsian ensemble description is introduced in terms of a multireplica stochastic master equation. The logarithm of the large time solution of the multireplica stochastic master equation is also a Lyapunov function, one for the stochastic evolution equations of the system. If the time dependence of the rate coefficients is generated by the variation of an external constraint, then the deterministic normal regime can be considered as representing the response of the system to an excitation, The coupling between the excitation and the system is nonlinear and multiplicative and generates interesting effects. A kinetic experiment is suggested for checking the existence of normal solutions for chemical systems with time-dependent rate coefficients.