  An isolated quantum system is considered, prepared in a nonequilibrium
initial state. In order to uniquely define the system dynamics, one has to
construct a representative statistical ensemble. From the principle of least
action it follows that the role of the evolution generator is played by a grand
Hamiltonian, but not merely by its energy part. A theorem is proved expressing
the commutators of field operators with operator products through variational
derivatives of these products. A consequence of this theorem is the equivalence
of the variational equations for field operators with the Heisenberg equations
for the latter. A finite quantum system cannot equilibrate in the strict sense.
But it can tend to a quasi-stationary state characterized by ergodic averages
and the appropriate representative ensemble depending on initial conditions.
Microcanonical ensemble, arising in the eigenstate thermalization, is just a
particular case of representative ensembles. Quasi-stationary representative
ensembles are defined by the principle of minimal information. The latter also
implies the minimization of an effective thermodynamic potential.
