The unifying scenario fo cosmic evolution is outlined by following the natural changes among radiation, matter and life in standard, big-bang cosmology. Using aspects of non equilibrium thermodynamics, especially energy flow considerations, we argue that it is the contrasting temporal behavior of various energy densities that have given rise to the environments needed for the emergence of galaxies, stars, planets, and life forms. We furthermore argue that a necessary (though perhaps not sufficient) condition--a veritable prime mover--for the emergence of such ordered structures of growing complexity is the expansion of the Universe itself. Neither demonstrably new science nor appeals to non-science are needed to explain the impressive hierarchy of generative change, from atoms to galaxies, from cells to society.