Irreversibility in the Derivation of the Boltzmann Equation

Uffink and Valente 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 discussion and a reply to that analysis. More specifically, I focus on two mathematical tools used in this derivation, viz. the Boltzmann–Grad limit and the incoming configurations. Although none of them are time-asymmetric ingredients, by themselves, I claim that the use of incoming configurations, as taken within the B–G limit, is such a time-asymmetric ingredient. Accordingly, this leads to reconsider a kind of Stoßzahlansatz within Lanford’s derivation.