A two-particle factorization condition enables an entropy dissipation inequality for non-reversible binary collision models in the Boltzmann equation, yielding an H-theorem.
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A variational principle selects the energy-conserving homogeneous Boltzmann equation, derives it from Kac's walk, and proves propagation of entropic chaoticity under minimal initial assumptions.
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Entropy dissipation inequality for general binary collision models
A two-particle factorization condition enables an entropy dissipation inequality for non-reversible binary collision models in the Boltzmann equation, yielding an H-theorem.
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Variational derivation of the homogeneous Boltzmann equation
A variational principle selects the energy-conserving homogeneous Boltzmann equation, derives it from Kac's walk, and proves propagation of entropic chaoticity under minimal initial assumptions.