There is an unfortunate problem with calling entropy a measure of disorder or randomness.

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There is an unfortunate problem with calling entropy a measure of disorder or randomness. One tends to think of entropy in terms of shuffling cards. As a matter of fact, that's usually how it is presented. However, there's something missing in that picture. What's missing is energy. A more real picture of the way entropy works is to think of two systems sharing energy. If you count the number of ways that the systems may share energy, the most probable configurations are the ones you'll see most frequently; the less probable ones will be ones you see less frequently. The entropy maximizes at the most probable state. If you look at real systems, they follow a particular trajectory through phase space. If the systems are such that the details of the interactions are not very important, but the statistics and dynamics are important, then the distributions of the observed macroscopic variables can be written directly in terms of the entropy (Omega(E) = exp(S(E)/k), where k = Boltzman's constant). In a sense, entropy is just a way to count up the number of ways or frequencies of being able to observe a system in some state given that its sharing energy with other systems. (Slight oversimplification, but not a bad starting point.) Those energies with large frequencies of observation are more 'random' than those with small frequencies. There's more ways for a bunch of molecules to fill a room than for them to pile up into a corner; the most probable states often look more random. However, as the Urey (sp?) experiments demonstrate, it is a mistake to simply assume that the second law implies that systems move from more complicated to less complicated (a particular interpretation of 'random' that has little to do with the actual definition of entropy) states.


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