Irreversibility in the derivation of the Boltzmann equation

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Ardourel, Vincent
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conference paper description
Uffink and Valente (2015) claim that there is no time-asymmetric ingredient that, added to the Hamiltonian equations of motion, allows to obtain the Boltzmann equation within the Lanford's derivation. This paper is a reply to that analysis. I claim that there are two main ingredients in the derivation of the Boltzmann equation with regard to the question of irreversibility. On the one hand, the use of the Boltzmann-Grad limit allows to derive equations that are not invariant under time reversal from equations that are time reversal invariant. On the other hand, the choice of incoming configurations instead of outgoing configurations to represent collisions between particles, is the time-asymmetric ingredient allowing to obtain the Boltzmann equation.