# The second law

1. Apr 7, 2005

### Palindrom

Hi all,

Can the second law of Thermodynamics be proven? (I mean, starting with the definition S=kln(Ohmega).)

If not.. is it just an empiric fact?

2. Apr 7, 2005

### dextercioby

Yes,the second law of thermodynamics can be proved via statistical methods for both reversible & irreversible processes...

Daniel.

3. Apr 7, 2005

### toffee

S=kln(Omega) is an empirical fact. But the 2nd law, both clausiius and Kelvins laws taken together, is just a statment that no engine can be 100% efficient.. its pretty easy to proove this: by a compostie system with a carnot and kelvin violator (i think)??

4. Apr 7, 2005

### dextercioby

Nope.In the axiomatical approach to equilibrium SM,Boltzmann's formula

$$S\left(E,V,N)=k\ln \Omega^{*}_{E,\Delta E} (E,V,N)$$

is just a result,a theorem if u prefer.

Nothing is "empirical" in SM...

Daniel.

5. Apr 7, 2005

### toffee

its a postulate - its consistent with what happens in nature. its not proovable is it?

6. Apr 7, 2005

### dextercioby

Experiments can confirm/infirm what a postulate afirms...But that doesn't make the postulate (in this case,the theorem) "empirical",by any means...

Daniel.

7. Apr 7, 2005

### ZapperZ

Staff Emeritus
You might want to read this:

http://arxiv.org/abs/cond-mat/0208291

Zz.

8. Apr 7, 2005

### Palindrom

First of all thanks to everyone.

dextercioby- you say Boltzmann's formula is a result. What is then the def. of entropy?

ZapperZ- Thanks, I'll go over it tommorow.
If it's not in ZapperZ's link, what is the proof then of the second law?
I asked my Prof. if it could be proved, and he told me it was an empirical fact. It seemed odd so I asked here. Seing he says it's empirical, I have little faith he's gonna prove it. And I have no intention to go through my first class of SM without knowing the proof...

9. Apr 7, 2005

### dextercioby

For a classical statistical equilibrium ensemble,the statistical entropy is defined as - Boltzmann's constant multiplied with the average* of the logarithm of the density probability.

Daniel.

-------------------------------------------
* average on the ensemble

$$S_{stat}=:-k\langle \ln\rho \rangle_{\rho}$$

10. Apr 7, 2005

### jdavel

Palindrom,

The empirical fact on which SM is based is that the energy (or at least part of the energy) contained in a system is the kinetic energy of random motion. From that point on, SM is just math, and therefore provable.

11. Apr 7, 2005

### dextercioby

SM is a theory.It's in the realm of theoretical physics.It has an axiomatic structure,just like QM,SR,GR,CM,...

As in any of the afore mentioned theories,math is extremey important,but physics is there,too...

Daniel.

12. Apr 8, 2005

### Palindrom

OK now it's getting interesting.
Do you have a recomendation for a good and high leveled book in SM?
I like to see the math in the physics btw, as well as the physics in the math.
Thanks everyone!

13. Apr 8, 2005

### dextercioby

3 volumes of Landau & Lifschitz's series are on SM...5,9 & 10.

For nonequilibrium SM,i'd vote for Balescu's "Equilibrium & nonequilibrium statistical mechanics".

Daniel.

14. Apr 8, 2005

### Palindrom

Thanks a lot!
I'll go find them tommorow.

Do you know F. Reif's "Fundamentals of Statistical and Thermal Physics"?
How is it?

15. Apr 8, 2005

### dextercioby

It's too easy.Meaning it's an introductory/undergraduate course,just like any of the 5 vols which compile the Berkley series.

Also F.Schwabl has a modern (new) text on SM.And Greiner has a very good calculatory book...

Daniel.

16. Apr 8, 2005

### Palindrom

Ok, so you've given me a few of books. Which one do you think I should start with?
I'd like to be able to go through it during this semester, and study from it. I don't really have time for more than 1 book...

Sorry for the multiple questions.

17. Apr 8, 2005

### dextercioby

Greiner is a good intro book.It has many applications...W.Greiner:"Thermodynamics and statistical mechanics",Springer Verlag.Any edition (i think there are only 2,but i'm not too sure).It's one of the books in the "Greiner series".

Daniel.

18. Apr 8, 2005

### Palindrom

Thanks a lot!