Kinetic theory modeling constitutive relations

In this section the elementary definitions and results deduced from the H-theorem are given [10]. In summary, the statistical //-theorem of kinetic theory relates to the Maxwellian velocity distribution function and thermodynamics. Most important, the Boltzmann s //-theorem provides a mechanistic or probabilistic prove for the second law of thermodynamics. In this manner, the //-theorem also relates the thermodynamic entropy quantity to probability concepts. Further details can be found in the standard references [20, 39, 55, 68, 90, 117, 150, 157]. In practice, during the process of developing novel models for the collision term, the //-theorem merely serves as a requirement for the constitutive relations in order to fulfill the second law of thermodynamics (in a similar manner as for the continuum models). 

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