# Exploring the Proof of the Second Law of Thermodynamics

• Palindrom
In summary, the second law of thermodynamics can be proven via statistical methods. It is an empirical fact, but the theorem that energy cannot be created or destroyed is just a result.
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?

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

Daniel.

Palindrom said:
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?

S=kln(Omega) is an empirical fact. But the 2nd law, both clausiius and Kelvins laws taken together, is just a statement 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)??

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.

dextercioby said:
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.

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

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.

Palindrom said:
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?

You might want to read this:

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

Zz.

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 going to prove it. And I have no intention to go through my first class of SM without knowing the proof...

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

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

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.

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.

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!

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.

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

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

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.

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.

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.

Thanks a lot!

## 1. What is the Second Law of Thermodynamics?

The Second Law of Thermodynamics states that in any isolated system, the total entropy (or disorder) will always increase over time. This means that energy will naturally flow from areas of higher concentration to areas of lower concentration, resulting in a decrease in usable energy.

## 2. How is this law proven?

The proof of the Second Law of Thermodynamics relies on statistical mechanics and probability. It can be mathematically proven that in a closed system, the number of possible microstates (or arrangements) of particles that result in a high entropy state is much greater than the number of microstates that result in a low entropy state.

## 3. What evidence supports the Second Law of Thermodynamics?

One of the most commonly cited evidence is the increase in entropy over time in various natural processes, such as the diffusion of molecules, heat transfer, and chemical reactions. This is observed in both macroscopic and microscopic systems and is consistent with the predictions of the Second Law.

## 4. Can the Second Law of Thermodynamics be violated?

No, the Second Law of Thermodynamics is considered a fundamental law of nature and has never been violated or disproven. However, it is important to note that the law applies to isolated systems, so it is possible to decrease entropy in a local system by inputting energy from an external source.

## 5. How does the Second Law of Thermodynamics relate to the concept of disorder?

The Second Law of Thermodynamics is often associated with the concept of disorder or randomness. This is because as entropy increases, the system becomes more disordered and less predictable. However, it is important to note that entropy is a measure of energy dispersal, not necessarily disorder. Some systems, such as crystals, can have low entropy but still exhibit a high degree of order.

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