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# Physics/Entropy of the Universe

Question
Hello,

For a system that is completely isolated from its surroundings, basic thermodynamics requires that the quasi-static heat flux dQ and the entropy change dS be related by:
dQ = TdS
and since the system is isolated,
dQ=dS=0
Therefore, an isolated system should be isentropic, that is, it's entropy must remain a constant.

The UNiverse is itself an isolated system (please don't bring up branes and stuff like that, let's keep it classical) - so there is no heat input or output. Consequently, the entropy of the Universe should also be constant.
However, my understanding of the second law is that the entropy of the Universe is always increasing. Further, many cosmological models require that the entropy of the universe increase drastically immediately after big bang.

Could you please explain if I am wrong somewhere and if so, how do I reconcile the two?

> there is no heat input or output.
> Consequently, the entropy of the Universe should also be constant.

You forgot something: our Universe may be isolated, but its density is decreasing.

Imagine an ideal gas within a thermally isolated container. The container is so small, however, that all gas molecules must be within a few diameters of each other. This means there are not "that many" ways the molecules can arrange themselves within the container; ie, there are not that many permitted states of the total system.
Now expand the volume of the container by a factor of ten. The molecules now have FAR more ways they can arrange themselves; ie, there are far more permitted states of the total system.

More permitted states => higher entropy. And ALL we did is decrease the density of the total system.

That's what happening in our Universe: the density if going down, the number of permitted states of all particles to arrange themselves are going up, and thus the entropy is going up as well.

That doesn't mean that PARTS of our Universe can't use gravitational potential energy to pull themselves together, and thus DECREASE the LOCAL amount of entropy. Or that the energy released from thermonuclear reactions can't be used by organic molecules to organize into more complicated molecules, thus decreasing the LOCAL entropy even more. But the TOTAL entropy of the entire Universe does, indeed, increase over time.

Physics

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