Heat death of the universe and the 3rd law of thermodynamics

[Robert Leslie]

If the universe keeps expanding and eventually ends in a "big freeze" or heat death, does this contradict the third law of thermodynamics?

The third law of thermodynamics states that a crystal at absolute zero has zero entropy. Since the entropy of the universe can never decrease, as the age of the universe approaches infinity, so will the entropy. However as the universe reaches heat death, and the stars burn out all their nuclear fuel, the temperature will also begin to approach absolute zero.

How can the temperature approach zero, and the entropy approach infinity at the same time? Does this contradict the third law of thermodynamics?

 

[Orodruin]

Since the entropy of the universe can never decrease, as the age of the universe approaches infinity, so will the entropy.

This is not true. You can have a monotonically increasing function that has a finite limit. Example: $\lim_{x\to\infty} \arctan(x) = \pi/2$. Also, a constant function does not decrease, but it does not go to infinity either.

Also, heat death does not imply zero temperature, although that is what you will get if the the Universe expands eternally. It is just what happens when the Universe comes to thermal equilibrium.

 

[Grinkle]

In a scenario where heat death is the state where the universe contains one particle per cosmic horizon, I am not sure there is a good way to evaluate either temperature or entropy. If heat death is some other scenario, I think both will have values that are not zero and not infinity respectively.

 

[kimbyd]

If the universe keeps expanding and eventually ends in a "big freeze" or heat death, does this contradict the third law of thermodynamics?

Yes and no.

The third law of thermodynamics is a classical law that doesn't take into account either gravity or quantum mechanics. So yes, it is literally true that it contradicts the third law, but the reason it does so is that it is invalid to apply the third law of thermodynamics to the universe as a whole.

In the far future, when the universe is essentially empty, its entropy will be given by the area of the cosmological horizon, which will be huge.

 

[hilbert2]

How can the temperature approach zero, and the entropy approach infinity at the same time? Does this contradict the third law of thermodynamics?

How do you deduce that all matter in the universe of far future will be in the form of perfect defect-free crystals? And even if it were, doesn't the energy that is in the form of photons and gravitational waves also contribute to the total entropy?