  The dissipative models in string theory can have more broad range of
application: 1) Noncritical strings are dissipative systems in the "coupling
constant" phase space. 2) Bosonic string in the affine-metric curved space is
dissipative system.
  But the quantum descriptions of the dissipative systems have well known
ambiguities. In order to solve the problems of the quantum description of
dissipative systems we suggest to introduce an operator W in addition to usual
(associative) operators. The suggested operator algebra does not violate
Heisenberg algebra because we extend the canonical commutation relations by
introducing an operator W of the nonholonomic quantities in addition to the
usual (associative) operators of usual (holonomic) coordinate -momentum
functions. To satisfy the generalized commutation relations the operator W must
be nonassociative nonLieble (does not satisfied the Jacobi identity) operator.
As the result of these properties the total time derivative of the
multiplication and commutator of the operators does not satisfies the Leibnitz
rule. This lead to compatibility of quantum equations of motion for dissipative
systems and canonical commutation relations. The suggested generalization of
the von Neumann equation is connected with classical Liouville equation for
dissipative systems.
