Abstract
A method is proposed to calculate the Boltzmann non equilibrium entropy as a Taylor series expansion in terms of the successive moments of the velocity distribution function. As a first application, the entropy of the BKW solution of the Boltzmann equation is calculated for both even and odd dimensions. The properties of the entropy of the Tjon Wu modeld=2) are studied and a quantitative condition is derived, showing that the McKean conjecture is incorrect. As a second application of the method, the entropy of one of the solutions of the very hard particle model for the Boltzmann equation is also derived.
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Tourenne, C.J. A method to calculate Boltzmann entropy. J Stat Phys 41, 335–348 (1985). https://doi.org/10.1007/BF01020618
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DOI: https://doi.org/10.1007/BF01020618