  We use the phase space position-velocity ($x,v$) to deal with the statistical
properties of velocity dependent dynamical systems, like dissipative ones.
Within this approach, we study the statistical properties of an ensemble of
harmonic oscillators in a linear weak dissipative media. Using the Debye model
of a crystal, we calculate at first order in the dissipative parameter the
entropy, free energy, internal energy, equation of state and specific heat
using the classical and quantum approaches. for the classical approach we found
that the entropy, the equation of state, and the free energy depend on the
dissipative parameter, but the internal energy and specific heat do not depend
of it. For the quantum case, we found that all the thermodynamical quantities
depend on this parameter.
