Statistical Physics on the space (x,v) for dissipative systems and study of an ensemble of harmonic oscillators in a weak linear dissipative medium

摘要

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