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Significance of n-sphere in statistical physics

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data

    Just trying to understand something my instructor said. For large n, the volume of the sphere exists in a thin shell at its surface. He asked us what relationship this has to statistical physics.

    2. Relevant equations

    3. The attempt at a solution

    The only thing I can think of is at very high numbers of dimension the volume of a sphere is akin to its surface area ??
     
  2. jcsd
  3. Apr 16, 2013 #2

    mfb

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    Imagine N particles with velocity v_i with a fixed total energy E. How does their phase space look like?
    How does the phase space (and its volume) look like if you reduce E a tiny bit?
     
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