# How does this new theory of a possible infinitely old universe not violate the second law of thermodynamics

I read the following article: http://phys.org/news/2015-02-big-quantum-equation-universe.html

And followed it back to this journal reference : http://arxiv.org/abs/1404.3093

It appears to be legitimate. I wonder how, in an infinitely old universe, the entropy in the universe is not also infinite considering that entropy always increases.

Edit: entropy is disorder so it increases to infinity rather than decreases to zero.

With regard to my question about entropy in a cyclical universe it appears that solution is to assume that the universe is not exactly the closed system we thought it was.

• Entropy in a cyclic universe is discussed here. The short answer is that dark energy provides a possible solution. The long answer can be found here. – lemon Feb 15 '15 at 18:38
• Related question about the merits of that paper: physics.stackexchange.com/q/164511/50583 That said, why would an infinitely old universe have a problem with having posivite energy? – ACuriousMind Feb 15 '15 at 18:39
• second law of thermodynamics states that entropy can only increase or stay constant. I do not understand your "how the entropy is greater than zero" question. – anna v Feb 15 '15 at 19:47
• can you clarify your question? do you mean why wouldn't an infinitely old universe be in a state of maximum disorder? why wouldn't it have reached equilibrium? – innisfree Feb 15 '15 at 20:35
• Infinity, in contrast to zero, is not a unique number. The limit of something takes you to infinity, and since the universe is supposed to be always there and no limit in time is envisaged, it just means that the entropy of the whole universe will be a very very large number. – anna v Feb 16 '15 at 7:22

Consider the function $e^x$: it is monotonically increasing and yet defined for all negative $x$.
• Now given a function defined on the real line augmented by the points at $-\infty$ and $+\infty$, you get a function defined on the semicircle. But since the semicircle is finite, you get something that's a little more agreeable to the intuition. – Leandro M. Feb 16 '15 at 20:59