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:The concepts of "disorder" and "spreading" can be analyzed with this information entropy concept in mind. For example, if we take a new deck of cards out of the box, it is arranged in "perfect order" (spades, hearts, diamonds, clubs, each suit beginning with the ace and ending with the king), we may say that we then have an "ordered" deck with an information entropy of zero. If we thoroughly shuffle the deck, the information entropy will be about 225.6 bits: We will need to ask about 225.6 questions, on average, to determine the exact order of the shuffled deck. We can also say that the shuffled deck has become completely "disordered" or that the ordered cards have been "spread" throughout the deck. But information entropy does not say that the deck needs to be ordered in any particular way. If we take our shuffled deck and write down the names of the cards, in order, then the information entropy becomes zero. If we again shuffle the deck, the information entropy would again be about 225.6 bits, even if by some miracle it reshuffled to the same order as when it came out of the box, because even if it did, we would not know that. So the concept of "disorder" is useful if, by order, we mean maximal knowledge and by disorder we mean maximal lack of knowledge. The "spreading" concept is useful because it gives a feeling to what happens to the cards when they are shuffled. The probability of a card being in a particular place in an ordered deck is either 0 or 1, in a shuffled deck it is 1/52. The probability has "spread out" over the entire deck. Analogously, in a physical system, entropy is generally associated with a "spreading out" of mass or energy.
:The connection between thermodynamic entropy and information entropy is given by Boltzmann's equation, which says that ''S = k<sub>B</sub>'' ln ''W''. If we take the base-2 logarithm of ''W'', it will yield the average number of questions we must ask about the microstate of the physical system in order to determine its macrostate.<ref>In classical mechanics the velocities and positions are real numbers, and there is a [[Continuum (measurement)|continuum]] of an infinite number of microstates. This would mean that an infinite number of questions would have to be asked in order to determine a macrostate. In quantum mechanics, the microstates are "quantized" and there are a finite number of them for a given energy, so the number of questions is finite. Boltzmann developed his theory before the advent of quantum mechanics, and it is to his credit that he was nevertheless able to develop a theory that dealt with a theoretically infinite number of microstates.</ref>
==See also==
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