We establish that the nonequilibrium dynamics of most pure states gives rise to the same entropy production as that of the corresponding ensemble, provided the effective dimension of the ensemble is large enough. This establishes the positivity of entropy production under a wide variety of nonequilibrium situations. Our results follow from dynamical typicality and suitable continuity properties alone, without relying on non-integrability, and they complement other recent efforts to establish "pure state second laws". An explicit comparison with the distinctively different two-point measurement scheme is also provided.

Slightly revised and accepted version. 4.5 pages main text with 1 figure plus 3 pages supplement with 1 figure