The term closed system means that energy enters and leaves the system boundaries (as light or heat) but mass does not. This is only an approximation because the earth is truly an open system, mass can enter and leave just like radiation, but its a good approximation because the amount of mass that enters in the form of meteorites and the amount of mass that leaves on rockets are very small compared to the overall mass of the earth so we can ignore mass transfer for purposes of explanation and focus on the incoming and outgoing radiation. So, the closed system has a few options with respect to overall energy flux. More energy can go in than comes out, in which case the temperature of the system will increase; more energy can go out than comes in, in which case the system will get colder; or the input and output can balance over time, in which case...you get it, the average temperature should stay the same. The earth is getting hotter by the way, and that’s a problem. But for the moment lets just focus on some short time scale during which life (and countless other irreversible processes) are going on on the earth but during which the average temperature of the earth is staying the same--Energy is being “processed” constantly by the biosphere, yet the total energy that comes into the earth and the total energy that leaves roughly balance out and energy is never lost--what is happening? In simple, physical terms the biosphere is converting light to heat. In the language of statistical thermodynamics, irreversible processes are producing entropy. Let me try to explain how these phrases are equivalent descriptions.