  We consider the class of non-Hamiltonian and dissipative statistical systems
with distributions that are determined by the Hamiltonian. The distributions
are derived analytically as stationary solutions of the Liouville equation for
non-Hamiltonian systems. The class of non-Hamiltonian systems can be described
by a non-holonomic (non-integrable) constraint: the velocity of the elementary
phase volume change is directly proportional to the power of non-potential
forces. The coefficient of this proportionality is determined by Hamiltonian.
The constant temperature systems, canonical-dissipative systems, and Fermi-Bose
classical systems are the special cases of this class of non-Hamiltonian
systems.
