[Pw_forum] a questoin about pressure and bulk modulus of system

[meysam pazoki]

Dear PWSCF users

I have a queston about bulk modulus and pressure of a system.
We know from thermodynamics that the energy of our electronic
system is E=TS-PV+μ N.In the zero temrature(T=0) we have E=-PV+μN and
p=-∂E/∂v.In the limit of born openhimer approximation with freezed ions, we
can calculate the pressure of our system(electrons+ions) by partial
derrivative of energy with respect to volume of system.But in literature I
see that calculate pressure from this term: p=-dE/dV and neglect the ∂E/∂μ
term.Is it correct?
In the zero temrature chemical potential is equal to fermi energy and We
should expect that the fermi energy have  no changes by variation in volume
of system.Is it correct for finite temratures,too?

Best Regards
Meysam Pazoki
SUT
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