Boltzmann distribution derivation.

[kidsasd987]

please check the video at 5:33.

how can we find the partial derivative w.r.t n1 n2 and on? isn't each state (n1, n2 and on) one discrete state not a continuous variable? is it because we can have multiple particles in the given energy state?

However its a finite discrete number. as far as I know, derivative is defined on continuous(complete) functions.

 

[BvU]

However its a finite discrete number. as far as I know, derivative is defined on continuous(complete) functions

Correct. But between 5:16 and 5:20 the transition from discrete to continuous is being made. The reason this can be done is that n is always large (and Stirling's formula is a good approximation)