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Is entropy a measure of disorder ?

  1. Jan 17, 2014 #1
    Is entropy a measure of "disorder"?

    In textbooks I never saw a definition of entropy given in terms of a "measure of disorder", and am wondering where this idea comes from? Clausius defined it as an "equivalent measure of change", but I do not see the relation with a concept of "order" or "disorder" which, as far as I know, are only intuitive concepts, not defined in physics. In statistical mechanics Boltzmann and Gibbs told us that there could be an interpretation of entropy as the logarithm of the number of possible microstates, but again, this isn't for me a definition for disorder. In fact, we could equally immagine a completely disordered system at (almost) absolute zero temperature and zero entropy, and nevertheless with a completely amorphous (i.e. disordered) crystal structure.

    And yet, lots of people, even renewed physicists, when they speak to the public, they continue to speak of entropy as a measure of disorder. I never could understand where this comes from? I understand that popularizing difficult concepts to an audience of non experts needs simplified analogies, but I think everyone could equally well have an intuitive idea of entropy as a "measure of change", or the "measure of all possible configurations". I simply perceive the identification of entropy with disorder simply as false and misleading. And what is surprising is that primarly professional physicists are responsible for this. Or.... am I missing something?
  2. jcsd
  3. Jan 17, 2014 #2


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  4. Jan 17, 2014 #3
    No, in information theory entropy could be seen something like as a measure of the lack (or amount) of information, which is in line with Boltzmann-Gibbs interpretation (where, in some sense, it may be seen as a measures of our ignorance of the real microstate of a system vs. all the possible microstates), but that has nothing to do with disorder. I could have all the information on the whereabouts of molecules and atoms in a frozen substance at almost absolut zero (i.e. with zero entropy), and yet with no crystal structure, a completely disordered and amorphous configuration.
  5. Jan 17, 2014 #4


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    It depends on what you call disorder. Take a well-shuffled deck of cards. I would call the deck "ordered" if for instance cards were in order of suit, or separated by color, or all aces, 2s, 3s, etc together. If you consider all the possible microstates, you will find that there are usually very few that you would called ordered out of the 52! possible combinations, so an ordered state is considered low entropy.

    Which is indeed a higher entropy state. See residual entropy.
  6. Jan 17, 2014 #5


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    An amorphous solid has a higher entropy than a crystal that has a regular lattice.

    The connection between entropy and disorder is that if a system is disordered, then it requires many parameters to completely describe its state. If you have 10^23 atoms with no particular pattern to their states, then a complete description of the state (classically) would require giving 10^23 positions and momenta. In contrast, if those atoms are arranged neatly into a crystal lattice, then describing the state only requires giving the number of particles and the dimensions of a single cell of the crystal.
  7. Jan 17, 2014 #6
    Ahh... ok. Now this sounds better... Thanks.
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