  A master equation for the deformed quantum harmonic oscillator interacting
with a dissipative environment, in particular with a thermal bath, is derived
in the microscopic model by using perturbation theory, for the case when the
interaction is deformed. The coefficients of the master equation and of
equations of motion for observables depend on the deformation function. The
steady state solution of the equation for the density matrix in the number
representation is obtained and shown that it satisfies the detailed balance
condition. The equilibrium energy of the deformed harmonic oscillator,
calculated in the approximation of small deformation, does not depend on the
deformation of interaction operators.
