2007•arXiv (Cornell University)Open access
On the equivalence of the microcanonical and the canonical ensembles: a\n geometrical approach
Ricardo López‐Ruiz, J. Sañudo, Xavier Calbet
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Abstract
In this paper, we consider the volume enclosed by the microcanonical ensemble\nin phase space as a statistical ensemble. This can be interpreted as an\nintermediate image between the microcanonical and the canonical pictures. By\nmaintaining the ergodic hypothesis over this ensemble, that is, the\nequiprobability of all its accessible states, the equivalence of this ensemble\nin the thermodynamic limit with the microcanonical and the canonical ensembles\nis suggested by means of geometrical arguments. The Maxwellian and the\nBoltzmann-Gibbs distributions are obtained from this formalism. In the\nappendix, the derivation of the Boltzmann factor from a new microcanonical\nimage of the canonical ensemble is also given.\n
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