Variational procedure for time-dependent processes

A simple variational Lagrangian for the time development of an arbitrary density matrix is discussed. The factorization of the density is employed for the purpose. It is found that only the kinetic energy is present in the Lagrangian. The formalism applies to the Navier-Stokes equations of hydrodynamics, pure and mixed state cases and transport theory. Results show that the variational proposal is tested on a two-level system.