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.
A., Zimmer J.;From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage, Communications in Mathematical Physics 307, 3, 791–815, 2011
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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.