# Explaining Arrow of Time with Entropy

I just watched [some BBC show] where the host talked about Arrow of Time, where by 2nd law of thermodynamics states that "nature" is always low entropy to high entropy OR "ordered/structured" to "unordered/unstructured" state.

The "intiutive" examples used, also found elsewhere, are events like iceberg "spontaneously" melting, but never freeze up again; perfume diffuse out of bottle but not entering back in it on its own; etc.

Then what about the other things that appear to naturally create order like formation of cells and life, crystallization, snowflakes etc?

Am I missing something?

• The instances you mention where entropy seems to go down are conpensated by entropy going up elsewhere. Life, our atmosphere and such also only maintain a low entropy because they are relying on the even lower entropy of sun light. Mar 7, 2011 at 22:03
• Also have a look at this. Mar 7, 2011 at 22:07

Raskolnikov's comments are exactly right. If you want more detail, I wrote a pedagogical note on precisely this subject for the American Journal of Physics a while back: Evolution and the second law of thermodynamics

On top of what has already been said before, it's worth noting that there are several different kinds of "arrows of time" in Physics:

Sure, Entropy is one of them, but there are others. And the way they interact is not necessarily something that's very well understood and/or explained.

Remember that popular analogies are always missing some of the more rigorous and technical aspects — so, take them with a grain of salt. ;-)

PS: Forgot to mention this book earlier, it's quite a gem: Evolution as entropy: toward a unified theory of biology.

Actually, you can maximize the Entropy OR minimize the Energy of a given system, in order to achieve an equilibrium state of the system.

Entropy is not quite understood even in scientific recent works. What we have are only different views of it. In my point of view, a better interpretation of what Entropy really is comes from the derivation of the Boltzmann Transport equation. In order to derive it, you must make an assumption that the momenta of two particles before and after a given collision between them are uncorrelated. In other words, you must assume that you lose spontaneously information on every collision. When you do this (with some other assumptions), you get an reasonable equilibrium solution to the equation and, what is better, the system may has an equilibrium solution. This loss of information one my argue that raises the entropy of the system, so the entropy may be interpreted as a measure of the lack of information about the system.

It doesn't implicate that to have maximum entropy (or minimum information about the system), the system SHOULD be on an unordered state. And to be more precise, this lack of "order" should be interpreted as lack of "information". Then, you can be happy again and fortunately accept life as an organized state of matter.

update: Everything said here should coexist with the comments of the other users...

To read further about entropy as information, take a look at Shannon information theory.

Best regards!

G.F.R Ellis and T.Rothman had an article on 'the crystalizing universe' arxiv 0912.0808 with a neat sentence "... the arrow of time arises simply because the future does not yet exist." That sounds like a pretty straightforward explanation.

• ""... the arrow of time arises simply because the future does not yet exist."" And Zenon demonstrated that that arrow does not move :=( Mar 9, 2011 at 19:49

The concept of entropy is only an approximation: it can only be defined exactly in the thermodynamic limit of an infinite number of degrees of freedom. The same thing is true of all thermodynamic concepts, including phase of matter, equilibrium, etc. Such an approximation is only valid within certain limits...when pressed outside of those limits it yields paradoxes, nonsense, etc., as first pointed out by Sir James Jeans when he talked about the paradox of the thermodynamic law of increasing entropy contradicting the time-invariance of mechanics. (It must be remembered in this context that Boltzmann's programme was precisedly to deduce the laws of thermodynamics, including this one, from the laws of mechanics at the micro-level.)

It follows from this that the so-called arrow of time is merely a useful approximation which is good for some practical purposes, but not necessarily all purposes. Therefore,

The answer is Yes: it is analogous to quantum measurement since the same thing could be said about quantum measurement. See my http://arxiv.org/abs/quant-ph/0507017 for more details and references, also http://arxiv.org/abs/1108.3151 for Jeans's approach to these thermodynamic questions.

Also relevant to « the arrow of time,» are Feynman's thoughts on quantum measurement:

Feynman, in his Path Integrals and Quantum Mechanics, said that the reason why Quantum Mechanics is deterministic when you look backwards, to the past, but only probabilistic when you look forward to measurement results in the future was «undoubtedly » due to the fact that measurements rely on amplification, and that what was lacking so far was a statistical mechanics of amplifying apparatus to understand this. Cf http://arxiv.org/abs/quant-ph/0502044 for exact references and more discussion of this. See also Allahverdyan, Balian, and Nieuwenhuizen, http://arxiv.org/abs/cond-mat/0203460

In my opinion, the very sane view of Jeans's about the status of thermodynamic concepts has been lost sight of (even by Balian) due to the lack of progress in proving Khintchine's conjectures.

A recent review on the theme Life, gravity and the second law of thermodynamics is the official position.

;-)
What do you think about the evolution of this scenario: A universe completely homogeneous with T=0, with gravitation and collisionless, all particles are distant one from the others, and by some misfortune one particle move away from his position. Can you imagine what can be the evolution of T?