Thermalization of a particle by dissipative collisions

@article{Martin1998ThermalizationOA,
  title={Thermalization of a particle by dissipative collisions},
  author={Ph. A. Martin and Jarosław Piasecki},
  journal={EPL},
  year={1998},
  volume={46},
  pages={613-616}
}
One considers the stationary state of a test particle immersed in a homogeneous fluid in equilibrium at temperature T, undergoing dissipative collisions with the fluid particles. It is shown that the corresponding linear Boltzmann equation still possesses a stationary Maxwellian velocity distribution, with an effective temperature smaller than T. This effective temperature is explicitly given in terms of the restitution parameter and the masses. 
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References

Kinetic approach to granular gases.
TLDR
A class of models of driven granular gases for which the stationary state is the result of the balance between the dissipation and the random forces which inject energies is introduced, which exhibit a genuine thermodynamic limit.