Emergent pseudo time-irreversibility in the classical many-body system of pair interacting particles

In this paper, the emergence of macroscopic-scale pseudo time-irreversibility is studied in closed classical many-body system pair interacting particles. First, exact continuum equations are derived to Hamiltonian dynamics without utilisation statistical mechanics. Next, it shown that momentum density field incorporates thermal degrees freedom considered scaling limit, and therefore initial condition indicated time-irreversible solutions may exist dynamical equations. Numerical evidence for pseudo-irreversible equilibration, heat transport provided. Finally, possible reasons numerically obtained non-diffusional relaxation macroscopic order discussed.