Exploring System Energy in Statistical Mechanics

[latentcorpse]

In my notes,

http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM3.pdf

on page 1 we are told we're dealing with systems of fixed total E but in the expilicit example on page 3, do we not find 4 different values for the total energy. how is this possible?

 

[Ben Niehoff]

Right. The point is to look at how many different microstates (arrangements of up/down spins) correspond to the same macrostate (total energy). This is used to give us entropy as a function of total energy, S(E).

Notice that total energy is still an input parameter. So once we find the function S(E), we can fix E to be any particular allowed value.

 

[latentcorpse]

yes but this is supposed to be an isolated system hence E is fixed

yet in the table we have E being -3mH, -mH +mH, +3mH which means it's not fixed. i guess i just can't really follow your argument sorry

 

[Ben Niehoff]

We're not talking about a single system, but an ensemble of many possible systems. Each of those systems has a different energy and entropy. Your notes describe how to find the entropy as a function of energy, S(E).

Once we know S(E), we can then calculate properties of any particular system of some given energy E.