# Another question from Ashcroft and Mermin: Fermi-Dirac Distribution

• I
Summary:
this time about fermi -dirac distribution
Good Day :

i reached the page 40 of Ashcroft Mermin book and after the equation 2.38 there is this expression of E(a,N) which is equal to Helmoltez Free energy F = U - TS , how this two terms F , E are related ? any one can provide adequate explanation , and few useful references

Best Regards
HB

anuttarasammyak
Gold Member
I do not have the book. What is a ?

ath stationary state of N-electron system

Lord Jestocost
Gold Member
Summary:: this time about fermi -dirac distribution

i reached the page 40 of Ashcroft Mermin book and after the equation 2.38 there is this expression of E(a,N) which is equal to Helmoltez Free energy F = U - TS , how this two terms F , E are related ? any one can provide adequate explanation , and few useful references
The sum in the denominator of eq. 2.38 is the “canonical ensemble partition function” Q(N, V, T) of the considered N-electron system at volume V and temperature T. From statistical thermodynamics one has for the Helmholtz free energy F(N, V, T) of a closed system: F(N, V, T) = -kT lnQ(N, V, T)

https://en.wikipedia.org/wiki/Helmholtz_free_energy

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