Entropy Confusion: Feynman's Explanation and My Question

[Count Iblis]

Are you kidding me? This is a joke, right?



Can you provide a reference for this outlandish statement?



You are completely changing the subject here. I never claimed one cannot describe a large number of discrete particles using statistical methods; I claim that a statistical description does *not* underlie thermodynamics. SM is *not* 'more fundamental' than thermodynamics. Thermodynamics does not 'emerge' from SM.

I suspect we are using different definitions of SM, and what it means for X to be the foundation of Y. My definitions have nothing to do with how scientists and engineers work in the subject areas in practice. What I'm saying is similar to the statement that physics is the foundation of chemistry and biology. This does not imply that chemist use the Schrödinger equation to calculate the properties of molecules. The fact that they don't doesn't mean that physics is not a foundation of chemistry.

 

[Studiot]

SpectraCat

What are you talking about? How could you possibly get that from what I wrote? Of course it's not at equilibrium! I challenged you to use stat mech to derive the rate constant.

OK well I stated that SM methods are also applicable to non equilibrium situations and offered an example

In particular they are not necessarily about equilibrium. SM can be and indeed is employed in non equilibrium situations.

Mix 1 mole of sodium hydroxide with 1 mole of hydrochloric acid.
You have a definite non equilibrium situation

Your response was to state that my example was inadequate (did not qualify) and to ask for, I presume another one.

Please give an example (what you have written below does not qualify).

Now addressing the second part of your statement above.
Why do you keep harping on about the 'rate constant' when I presume you know that it applies strictly to equilibrium situations?
Are you actually asking me to set up and solve the relevant differential equations (which involve this constant) that do lead to the actual rate of reaction?


I wonder if, as you yourself observed so well in your post #29 that we are working on different interpretations of Statistical Mechanics?

Taking Andy’s definition form his post #31 (I agree with this)

Statistical Mechanics: (classical or quantum) mechanics of a large number of discrete particles.

I think my example qualifies as it is the average action of some 10²⁴ molecules.

This is not about partition functions, energy surfaces or whatever – though we could discuss those.

 

[Andy Resnick]

I suspect we are using different definitions of SM, and what it means for X to be the foundation of Y. My definitions have nothing to do with how scientists and engineers work in the subject areas in practice. What I'm saying is similar to the statement that physics is the foundation of chemistry and biology. This does not imply that chemist use the Schrödinger equation to calculate the properties of molecules. The fact that they don't doesn't mean that physics is not a foundation of chemistry.

That's all well and good to have an idiosyncratic point of view...which you do not divulge except for an opaque metaphor... but it makes meaningful communication impossible.

 

[Andy Resnick]

SpectraCat



OK well I stated that SM methods are also applicable to non equilibrium situations and offered an example

<snip>

That was a poor example. To wit; you offered an example from *kinetics*. Kinetics is steady-state.

The reason steady-state can be modeled in SM is because it can be transformed to appear like *equilibrium*. Kinetics is a linearized theory- steady-state conditions are a linear condition.

You never responded to my example: calculate Q(t) for the OP's problem.

 

[SpectraCat]

SpectraCat



OK well I stated that SM methods are also applicable to non equilibrium situations and offered an example



Your response was to state that my example was inadequate (did not qualify) and to ask for, I presume another one.



Now addressing the second part of your statement above.
Why do you keep harping on about the 'rate constant' when I presume you know that it applies strictly to equilibrium situations?
Are you actually asking me to set up and solve the relevant differential equations (which involve this constant) that do lead to the actual rate of reaction?


I wonder if, as you yourself observed so well in your post #29 that we are working on different interpretations of Statistical Mechanics?

Taking Andy’s definition form his post #31 (I agree with this)



I think my example qualifies as it is the average action of some 10²⁴ molecules.

This is not about partition functions, energy surfaces or whatever – though we could discuss those.

You haven't said anything about "average action of molecules" until this very last post, and you still haven't said anything detailed about how your example has anything to do with the discussion at hand, which as I understand it, has two facets: first, whether or not thermodynamics can be derived from statistical mechanics alone, and second, whether or not chemical kinetics can be derived from statistical mechanics alone. I have largely stayed out of the first discussion, but I have been participating in the second.

My point all along has been that *if* statistical mechanics by itself were enough to explain all of chemical kinetics, then one should be able to take any system at any point in time, like your example of 1M HCl mixed with 1M NaOH at the moment of mixing, and using just the molecular-scale description of the system, write down equations for the time-evolution of the chemical species in the system so that its state at any other time could be accurately predicted, including any environmental effects such as changes in temperature, solvent composition, ionic strength, etc. To my knowledge, this cannot be done in the general case, starting from statistical mechanics. Of course I don't want you to actually do this, I just wanted to illustrate the difficulty (impossibility) of the task.

Your point is taken with regard to my use of the term "rate constant" in the second post .. notice that in my original post, I asked you to describe the "reaction rate", which is what I meant in my second post as well.

I don't think this has anything to do with us having "different definitions of SM" ... I too basically agree with what Andy wrote in post #31, although I would also stipulate that SM as applied often necessarily involves significant simplifications/idealizations of the underlying molecular physics (e.g. approximation of molecular vibrations as uncoupled harmonic oscillators), which can lead to significant deviations with respect to real systems.

 

[Studiot]

You haven't said anything about "average action of molecules" until this very last post

My understanding of the average action of a large numebr of particles or molecules is that this is what is meant by a statistical approach.

and you still haven't said anything detailed about how your example has anything to do with the discussion at hand, which as I understand it, has two facets: first, whether or not thermodynamics can be derived from statistical mechanics alone, and second, whether or not chemical kinetics can be derived from statistical mechanics alone

No indeed I didn't say much about the CT v SM debate. I felt others had already said more than enough about that issue already.

In fact I watched this thread for a while before saying anything at all. When I did, others were already discussing the original issue ( which was neither of the above) in minute detail. My aim was to extend the horizons somewhat and point out there are wider aspects, although remaining relevant to the original OP. I was not intending to do his homework for him.

I agree my claim about chemical engineering to be rather grandiloquent, but it was only a throwaway statement tacked on the end of something solid, not a bone to be latched onto.

That was a poor example. To wit; you offered an example from *kinetics*. Kinetics is steady-state.

The reason steady-state can be modeled in SM is because it can be transformed to appear like *equilibrium*. Kinetics is a linearized theory- steady-state conditions are a linear condition.

I really have no idea what you mean by this so would be grateful for an explanation.

In my book chemical kinetics is a single or system of differential equations of rate of change of concentration v time. These may be linear or non linear; obviously linear is preferable but many have to be solved numerically. these are all derived from the statistical observation that the rate of reaction (=rate of change of concentration) is proportional to some function of the concentration, linear if you are lucky.

However I don't see whether being linear or not has any bearing on the state of equilibrium or non equilibrium. I notice this 'requirement' has been dropped for SM but I don't understand what you mean by 'steady state' ?

 

[Andy Resnick]

Enough. Both of you (Studiot and Count Iblis) have oscillated between making grandiose claims (e.g., SM is a more fundamental theory than thermodynamics) while offering the most threadbare meager evidence (10% of a single book, kinetic theory, silence), and constantly switching the topic around.

I don't have a problem with students that do not know things; I do have a problem with your apparent inability to google "non equlibrium statistical mechanics". If you did, you would see that there is quite a lot of research on the subject- did you think I am the first person to point out deficiencies in SM?- and honestly, I would have been thrilled to have a discussion about mode coupling theory, the Fokker-Planck equation, Smoluchouski equation, and the fluctuation-dissipation theorem.

Neither of you have done any effort to learn anything new. All I see is the constant re-packaging of dried-up undergraduate elementary concepts held up as exemplars of physical theory. This is, frankly, an insult to those of us who actually do research.

I do not have the time or effort to teach the willfully ignorant. Maybe after you have done some learning we can try again.

 

[Mute]

I haven't given anyone a chance to respond, but I feel like I have been having this argument for over a month and not getting anywhere.

So, here's a simple challenge: solve this, and I will reconsider my earlier claims.

Using SM, solve either Q(t) or T(t) in the OP's question. If SM is truly a more fundamental theory than thermodynamics, this should be trivial.

Perhaps you should specify what exactly you have in mind when you say "fundamental", because I get the impression it is not what everyone else means when they say fundamental. It seems that you feel that a theory is more fundamental if it is more useful; this is not generally what people have in mind when they use that word.

Generally, a "fundamental theory" is taken to mean the "more real theory", in the sense that it is a more accurate description of Nature in principle. This does not necessarily mean it makes more accurate predictions. String Theory, were it to somehow be verified, would be considered the most fundamental theory, but no one would every dream of trying to calculate the trajectory of a baseball using it.

SM is considered more fundamental than Thermodynamics because it starts from a microscopic perspective and works up to the macroscopic quantities. Thermodynamics, on the other hand, is phenomenological, and having disposed of the need to have a microscopic description it is able to describe phenomena for which the microscopic picture is either unknown or exceedingly complicated. Similarly, Phenomenological Landau Theory is often more useful than starting with a microscopic Hamiltonian, but it wouldn't generally be considered "more fundamental".

So, if SM cannot be used to calculate your requested quantities, that says nothing of its "fundamental-ness" in the usual use of the term. So, what exactly do you mean by "fundamental"?

 

[Studiot]

This will be the second time I have quoted the Bible in this thread.

Despite suffering rudeness and dismissive arrogance by the Science Advisor I have decided to turn the other cheek and walk away, as advised in the introductory sticky notices.

 

[Count Iblis]

This will be the second time I have quoted the Bible in this thread.

Despite suffering rudeness and dismissive arrogance by the Science Advisor I have decided to turn the other cheek and walk away, as advised in the introductory sticky notices.

Yes, and also the entropy in this thread is just too high to have a meaningful discussion. And now that Mute has backed my general position, I think this is a good point to stop this discussion in this thread. Perhaps we can start another thread about the foundations of thermodynamics, statistical mechanics etc. etc.