Mathematical formalism of classical and statistical thermodynamics

[Sojourner01]

Does anyone else have a lot of trouble comprehending the derivations in statistical mechanics?

To me the mathematics feels somewhat archaic. Somehow it just seems as though it'd be neater if it was dealt with using matrix or operator methods. I always have trouble with the concept of entropy. If something can't be directly measured and isn't a real property, why bother calling it anything at all? Just impose boundary conditions on your equations of state and be done with it. I'm not saying thermodynamics is wrong, just that it does things in clunky and unintuitive ways.

Thermodynamics and Statistical Mechanics are by far my hardest classes. We had trouble with this lecturer last year; the trouble is, I can't put my finger on what it is he's doing wrong.

 

[marcusl]

Somehow it just seems as though it'd be neater if it was dealt with using matrix or operator methods.

Stat mech applied to quantum systems commonly uses operators and density matrices. That always comes after you've learned thermo and classical stat mech, however.

I always have trouble with the concept of entropy. If something can't be directly measured and isn't a real property, why bother calling it anything at all?

It's one of the most useful quantities around! It would be very awkward to use if it had no name...

I'm not saying thermodynamics is wrong

That's a relief!

Sometimes a different book can help. Reif explains things at great length which drives some people crazy but for decades others have turned to it for help.

 

[StatMechGuy]

The primary reason you don't see a lot of operators in statistical mechanics is that either (1) the formalism is overkill for the simpler problems or (2) the formalism requires a familiarity with things like Green functions and temperature Green functions and the like, which is a semester or two of classwork in itself.

Also, I recommend that you look up Lars Onsager's original solution of the Ising model. It does not involve the standard combinatorial approach, but he invented infinite loop algebras of operators to solve the problem. You will get more than your fill of using operators in statistical mechanics from that paper alone.