Boltzmann’s equation ruling the time evolution of the one-particle distribution function is obtained by partitioning the phase space into the free-flight and collision domains in low-density gases. The expressions for the entropy production and the entropy exchange are related to the H-theorem. The transport properties and gas-surface interactions are discussed. Furthermore, the multivariate fluctuation relation for the energy and particle fluxes is deduced from the fluctuating Boltzmann equation. In addition, an integral fluctuation relation is established for the Boltzmann factorization of the multiparticle probability density into one-particle distribution functions.