Can the Second Law of Thermodynamics Be Proven Empirically?

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Discussion Overview

The discussion centers on the provability of the second law of thermodynamics, particularly in relation to its definition involving entropy and statistical mechanics. Participants explore whether the law can be proven empirically or if it remains an empirical fact, touching on theoretical implications and foundational concepts in statistical mechanics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question whether the second law of thermodynamics can be proven, suggesting it may only be an empirical fact.
  • Others argue that the second law can be proved using statistical methods for both reversible and irreversible processes.
  • There is a claim that Boltzmann's formula is a theorem rather than an empirical result, indicating a distinction between theoretical and empirical aspects of statistical mechanics.
  • Some participants assert that while experiments can confirm or challenge postulates, this does not render them empirical in nature.
  • A participant references a professor's view that the second law is an empirical fact, expressing skepticism about its proof.
  • There is a discussion about the definition of entropy and its relation to statistical mechanics, with some participants seeking clarity on foundational concepts.
  • Recommendations for advanced texts in statistical mechanics are provided, indicating a desire for deeper understanding and mathematical rigor.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the second law of thermodynamics can be proven or if it is merely an empirical fact. Multiple competing views remain regarding the nature of the law and its foundational principles.

Contextual Notes

Participants express varying interpretations of statistical mechanics and its axiomatic structure, highlighting the complexity of proving the second law and the role of empirical evidence versus theoretical frameworks.

Who May Find This Useful

This discussion may be of interest to students and professionals in physics, particularly those focused on thermodynamics and statistical mechanics, as well as individuals exploring the philosophical implications of empirical versus theoretical knowledge in science.

Palindrom
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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?
 
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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

[tex]S\left(E,V,N)=k\ln \Omega^{*}_{E,\Delta E} (E,V,N)[/tex]

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

[tex]S\left(E,V,N)=k\ln \Omega^{*}_{E,\Delta E} (E,V,N)[/tex]

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

[tex]S_{stat}=:-k\langle \ln\rho \rangle_{\rho}[/tex]
 
  • #10
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
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
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.
So how about that book?
Thanks everyone!
 
  • #13
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
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
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
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
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
Thanks a lot!
 

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