# 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.

Edit 2: Thank you for the links to related questions about this article and chats. It appears to me that the likelihood of this theory being correct is quite low.

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

## 1 Answer

Consider the function $e^x$: it is monotonically increasing and yet defined for all negative $x$.

Just because something increases monotonically doesn't mean it must reach infinity (or even its maximum value) in a finite amount of time.

As a side note, please don't refer to entropy as disorder. It's very common but also very wrong: https://www.youtube.com/watch?v=vSgPRj207uE

• Excellent point. In order for a monotonically increasing function to not reach infinity, the rate of increase must approach 0 over an infinite amount of time. It is hard to wrap my head around actually standing at time = infinity. We aren't approaching infinity, we've already arrived there. Doesnt that mean the rate of entropy increase can't still be approaching 0, it must be 0. – Doug Coburn Feb 16 '15 at 17:15
• Perhaps the following idea will help. Instead of trying to think about the entire real line, imagine that you place a circle with radius 1 tangent to it at the origin. Now given a point on the real line, you can draw a line from it to the center of the circle. Note where the line crosses the circle: that gives a one to one correspondence between points on the line and points on the bottom semicircle, except for the two points on the "equator" which would correspond to minus and plus infinity respectively. – Leandro M. Feb 16 '15 at 20:56
• 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
• I'm sorry to disagree, but it seems to me that a mathematical evidence does not, necessarily, prove a physical problem. You cannot compare an abstract concept of 'e' to the 'x' and its behaviour towards minus infinite to something concrete as the time in the universe. Infinity concept of mathematics is abstract and should not be understood as a feasible reality. – PDuarte Apr 25 '18 at 15:54
• "You cannot compare an abstract concept of 'e' to the 'x' and its behaviour towards minus infinite to something concrete as the time in the universe." Seems I can, because I just did! – Leandro M. Apr 26 '18 at 17:27