Steady solutions of the BBGKY hierarchy and first integrals of the motion of a system of classical particles One-dimensional case

Steady solutions of the BBGKY hierarchy in one-dimensional classical statistical mechanics are studied. It is shown that every steady solution which satisfies a certain set of conditions is associated with a first integral of the motion of a finite system of particles. This eliminates one of the restrictive conditions that occur in an analogous theorem proved earlier by the author and Gurevieh [2].