Irreversibility paradox revised: onset of a center manifold in dissipative systems

A center-manifold-reduced Fokker-Planck equation is derived, starting from a time-reversible Liouville equation. The derivation is valid when there is a large separation of relaxation-time scales causing the phase-space contraction near a dynamic critical point. The paradox of breaking of time-reversal symmetry in the resulting Fokker-Planck equation at the onset of the center manifold is clarified