That seems to be my catch phrase for the CO2 warming purists. Energy in is equal to Energy out is the mantra of the Astrophysicists that have empowered carbon dioxide to control our little internal environment.
Over some period of time, Ein will eventually equal E out. Then at some time E out will be greater than E in, infinity is a long time after all. So Ein=Eout is conditional, not a physical law.
The standard condition is Ein=Eout plus delta S. Toward the end game of a planet or a star, delta S (dS) increases. The system can respond and collapse, delta S did not go negative, the system stored energy which can be work. That stored energy changes the internal system balance, which can result in spectacular events, like a super nova. That's when delta S peaked.
Early in the life of the system Ein > Eout, the system gains energy. Ein = Eout + dS, but how can a system gaining energy have a positive Entropy? If can't, the energy gained is work.
So the system is looking for a balance, a point where the work and the entropy are equal, then and only then does Ein=Eout. So the completed equation would be Ein +W=Eout+S or Ein=Eout +S-W, the real question is not what Ein or Eout are, but how large are S and W?
Since in equilibrium, S=W and Ein=Eout, then S/(S+W)=W/(S+W)=50 percent. That is the maximum entropy and work at equilibrium. There is no physical law that Ein=Eout only that at EQUILIBRIUM, Ein=Eout. If there is not work or stored energy in the system that is the only equation needed. If there is work done or energy stored, then Ein=Eout +S-W is the correct equation.
For a system where Ein=Eout and there is no work, then the system can be averaged simply to show that energy of one form is converted to energy of another form and that therefore energy is fungible and can take various forms provided Ein=Eout. Work complicates the issue be requiring different time constraints and conversions to be considered, potential energy, kinetic energy, chemical energy, biological/chemical energy in addition to electromagnetic.
The atmosphere has stored potential energy. If the steady state flow of energy through the atmosphere changes, then that potential energy can be converted downward to transfer energy back into the system or the potential energy can increase to store more energy. Both process would lose some energy to entropy, but some would be retained. Water contains energy, about 4.2 Joules per gram, it can store energy through phase change into ice 334 Joules per gram, evaporation 2400 to 2100 Joules per gram. This energy stored or released takes place at various rates, at various locations at various times, so it cannot be simply averaged. The type, time and place of the work has to be considered, so it is not SIMPLY fungible.
Energy is fungible under specific conditions, Work has different conditions, so energy is fungible but the work done is not.