  The Steepest Entropy Ascent approach is considered and applied to few-state
systems. When the Hamiltonian of the system is time dependent, the principle of
maximum entropy production can still be exploited; arguments to support this
fact are given. In the limit of slowly varying Hamiltonians which allows for
the adiabatic approximation for the unitary part of the dynamics, the system
exhibits significant robustness to the thermalization process. Specific
examples such as a spin in a rotating field and a generic two-state system
undergoing an avoided crossing are considered.
