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Why is the probability for say the Ising model to be found in state of energy E proportional to $e^{-E/kT}$ ?

Is this some postulate or can it be derived from simpler principles?

Sofia
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    are you asking for the Boltzmann factor in general or in a specific case? In the former case, related: http://physics.stackexchange.com/q/161269/58382 and http://physics.stackexchange.com/q/61936/58382 – glS Jan 29 '15 at 18:45
  • Have a look at section 1 of http://www.damtp.cam.ac.uk/user/tong/statphys/sp.pdf; it's a standard derivation. – JamalS Jan 29 '15 at 18:49

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The first law of thermodynamics is that energy is conserved. The second law of thermodynamics states that entropy never decreases. Therefore the equilibrium distribution must maximize entropy while maintaining the same average energy. For a given energy $U$, the distribution that does this is an exponential distribution.

Robin Ekman
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