Abstract

This work concerns David Hilbert’s sixth problem in mathematical physics and the kinetic theory of gases. Influenced by Maxwell, Boltzmann published in 1872, a fundamental equation describing the evolution of the density of probability in six-dimensional space of a particle velocity and position as a function of time. It is a non-linear integro-differential equation, difficult to solve. Boltzmann proved that it is an irreversible process towards equilibrium. We shall analyze Boltzmann’s equation and its iterative solution by Chapman and Enskog in 1916–1917, and the hot scientific discussions concerning the reversibility in time of a process, and the irreversibility of the Boltzmann equation. Finally, we present Anatoly Vlasov, a Russian physicist who adapted the Boltzmann equation to ionized gases in 1938.