X-Message-Number: 20857 Date: Mon, 13 Jan 2003 18:52:22 -0800 (PST) From: Driven FromThePack <> Subject: re: ettinger on heat death of the universe From another forum, a poster replied to Mr Ettinger's post on thermodynamics and the heat death of the universe. Here are some excerpts from that post: Quoting Mr Ettinger: "Actually, entropy is a concept poorly understood by most people...." The reply: .... This indicates a basic misunderstanding most people have with entropy. This is because very often people are not taught the connection between microscopic states, and entropy associated with a macroscopic state. You...are making a really fundamental mistake based on the fact that you completely do not understand what entropy really is. Now, Boltzmann tells us that when all configurations are equally likely, S = k ln W where k is Boltzmann's constant and W is the number of states accessible to the system. [This] means that the more states that are accessible to the system, the higher the entropy. Another way to think of this is the broader the probability distribution, the higher entropy is. .... a macroscopic example first. I have N books on my shelf, which I can order in N! ways. Let's ask a question. What is the entropy of the current arrangement? Well, S = k ln W. What's W? Well, when I say the current arrangement of my bookshelf, I am applying a constraint. That is, I'm saying, my books as currently ordered. In other words, there is 1 configuration possible. So the entropy is 0. In other words, it doesn't matter how "disordered" my books are; if I find the entropy of their current state, it's 0. This is the same as the entropy of the books if put in alphabetical order (assuming I have no duplicates). On the other hand, what is the entropy of all possible configurations? In this case, I can arrange my bookshelf in N! possible ways, so the entropy is k ln N! which is larger than 0 as long as N > 1. Here's why this is important: talking about the entropy of a specific configuration or state is [wrong]. It tells you nothing. One state is not inherently more ordered or less ordered than another. .... so how do we evaluate entropy? Well, we can do that because we never actually know the EXACT state of a system. If we know that we have 2 liters of helium gas at 298 K, we can call that our "state" of the system. But factually, we don't know the exact microscopic state of the system. We don't know where each gas molecule is. And frankly, we don't care. Because talking about the entropy of a single configuration doesn't make any sense; it's zero. When we talk about the entropy of our system, we are talking about all possible configurations which are accessible to the system. Now what does the second law say? It says that over time, you expect your system to maximize its probability distribution. That is, over time, you would expect your system to try and explore as much of configuration space as it can. You would *not* expect, for instance, that if you had a 2 L tank that your gas would stay on one side of the tank for an arbitrarily long time, leaving one liter of vacuum on the other side. Now, imagine that our gas molecules in the two liter tank had M possible configurations, with an entropy of S = k ln M. Now, how could we make the entropy decrease? There's only one way--we have to decrease the number of possible configurations it can visit. And in order to do that, we need to impose some restrictions on our system that would prevent it from entering some of those configurations. Once you impose those restrictions, though, you are no longer in an equilibrium state. So the state of highest entropy is always the equilibrium state. Now what you claim above is that you start in one configuration, which you say is "highest entropy". That you eventually must move from this state, implying entropy decreases. This is completely wrong, because you're mixing up microscopic configurations with macroscopic descriptions of entropy. .... __________________________________________________ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=20857