We maximize Shannon conditional entropy when the mean value of the random variables "state energy" and "number of particles in the state" are assigned. As particular cases, we derive the Bose-Einstein, Fermi-Dirac and intermediate statistics. Two assumptions have been introduced in order to guarantee the existence of the Lagrange multipliers; these latter are interpreted as sufficient conditions for the thermodynamical equilibrium. Neither Sstirling formula nor the the hypothesis of contninuous numbers are used.
Maximizing Conditional Entropies: a Derivation of Quantal Statistics
SEMPI, Carlo
1976-01-01
Abstract
We maximize Shannon conditional entropy when the mean value of the random variables "state energy" and "number of particles in the state" are assigned. As particular cases, we derive the Bose-Einstein, Fermi-Dirac and intermediate statistics. Two assumptions have been introduced in order to guarantee the existence of the Lagrange multipliers; these latter are interpreted as sufficient conditions for the thermodynamical equilibrium. Neither Sstirling formula nor the the hypothesis of contninuous numbers are used.File in questo prodotto:
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