  We discuss the r\^ole of quantum deformation of Weyl-Heisenberg algebra in
dissipative systems and finite temperature systems. We express the time
evolution generator of the damped harmonic oscillator and the generator of
thermal Bogolubov transformations in terms of operators of the quantum
Weyl-Heisenberg algebra. The quantum parameter acts as a label for the
unitarily inequivalent representations of the canonical commutation relations
in which the space of the states splits in the infinite volume limit.
