söndag 24 februari 2013

2nd Coming of the 2nd Law

The 2nd Law of Thermodynamics has remained as a main mystery of physics ever since it was first formulated by Clausius in 1865 as non-decrease of entropy, despite major efforts by mathematical physicists to give it a rational understandable meaning.

The view today is, based on the work by Ludwig Boltzmann, that the 2nd Law is a statistical law expressing a lack of precise human knowledge of microscopic physics, rather than a physical law independent of human observation and measurement. This view prepared the statistical interpretation of quantum mechanics as the basis of modern physics.

Modern physics is thus focussed on human observation of realities, while classical physics concerns realities independent of human observation. To involve the observer into the observed makes physics subjective which means a depart from the essence of physics of objectivity. A 2nd Law based on statistics thus comes along with many difficulties, which ended Boltzmann's life, and it is natural to seek a formulation in terms of classical physics without statistics.

Such a formulation is given in Computational Thermodynamics based on the Euler equations for an ideal compressible gas solved by finite precision computation. In this formulation the 2nd Law is a consequence of the following equations expressing conservation of kinetic energy K and internal (heat) energy E:
  • dK/dt = W - D
  • dE/dt = - W + D
  • D > = 0,  
where W is work and D is nonnegative turbulent dissipation (rates). The crucial element is the turbulent dissipation rate D which is non-negative, and thus signifies one-way transfer of energy from kinetic energy K into heat energy E.

The work W, positive in expansion and negative in compression, allows a two-way transfer between K and E, while turbulent diffusion D >= 0 can only transfer kinetic energy K into heat energy E, and not the other way.

We compare dE/dt = - W + D or rewritten as dE/dt + W = D as an alternative formulation of the 2nd Law, with the classical formulation found in books on thermodynamics:
  • dE + pdV = TdS = dQ
  • dS > = 0, 
where p is pressure, V is volume (with pdV corresponding to W), T is temperature, S is entropy and dQ added heat energy.

We see that D >= 0 expresses the same relation as dS >= 0 since T > 0, and thus the alternative formulation expresses the same effective physics as the classical formulation.

The advantage of the alternative formulation is that turbulent dissipation rate D with D >= 0 has a direct physical meaning, while the physical meaning of S and dS >= 0 has remained a mystery.

The alternative formulation thus gives a formulation in terms of physical quantities without any need to introduce a mysterious concept of entropy, which cannot decrease for some mysterious reason. A main mystery of science can thus be put into the wardrobe of mysteries without solution and meaning, together with phlogistons.

Notice the connection to Computational Blackbody Radiation with an alternative proof of Planck's radiation law with again statistics replaced by finite precision computation.

For a recent expression of the confusion and mystery of the 2nd Law, see Ludwig Boltzmann: a birthday by Lubos.

PS1 The reason to define S by the relation dE + pdV = TdS is that for an ideal gas with pV = RT this makes dS = dE/T + pdV/T an exact differential, thus defining S in terms of T and p. The trouble with S thus defined, is that it lacks direct physical meaning.

PS2 Lubos refers to Bohr's view of physics:
  • There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature...
This idea has ruined modern physics by encouraging a postmodern form medieval mysticism away from rational objectivity as the essence of science, where the physical world is reduced to a phantasm in the mind of the observer busy counting statistics of non-physical micro states.

PS3 Recall that statistics was introduced by Boltzmann to give a mathematical proof of the 2nd law, which appeared to be impossible using reversible Newtonian micromechanics, followed by Planck to prove his law of radiation, followed by Born to give the multidimensional Schrödinger equation an interpretation. But this was overkill. It is possible to prove a 2nd law and law of radiation using instead of full statistics a concept of finite precision computation as shown in Computational Thermodynamics and Computational Blackbody Radiation, which maintains the rationalism and objectivity of classical mechanics, while avoiding the devastating trap of reversible micromechanics.  

24 kommentarer:

  1. Exactly where is the confusion and mystery in the last link you give to the blog-post by Motl?

    Reading the post it lucidly explains where the confusion about the second law originates (you seem to run into this trap your self looking at your presented theory) and it dispels any mystery. Or it certainly will in near future, if one look at one of the first comments, coarse-graining is mentioned and the original writer mention a will to write a specific blog-post touching upon this.

    Oh, and a final question. How does your version of the second law work in a solid?

  2. Friction is for a solid friction what corresponds to turbulent diffusion for a gas. The confusion with statistics is that statistics is done by humans but not by physical objects. If you believe in physics independent of human observation, statistics is not an option. If you think that you are the center of the universe, statistics is fine.

  3. Did you read the blog-post that you refer to?

  4. The post is a repetition of standard statistical mechanics, which in my opinion is not physics.

  5. That was the point...

    Statistical mechanics are neither confusing or mysterious.

    That you doesn't consider it to be physics is more your loss then those who use it as an indispensable tool in describing and predicting nature.

  6. Yes, maybe it reflects a limitation of my mind. But all that glitters in mechanics is not gold, according to Schrödinger and Einstein...

  7. In your opinion, what kind of theory should one use on length and time scales where continuum mechanics breaks down? What is the physical meaning of D in those regimes?

    The theory you present here looks exactly as the second law defined from a dissipation function originating from mass, momentum and energy conservation in a fluid. This is in the curriculum in an ordinary master level course in continuum mechanics. What is new?

  8. A proper version of the Schrödinger equation may be used. This is also a continuum model and as such subject to the presence of D as a reflection of impossibility to exactly satisfy the conservation law expressed by Schrödingers equation, which reflects the ,inevitable appearance of turbulence in systems with many components/particles/atoms. The novelty in our approach is to give the dissipation a meaning as reflecting an impossibility of satisfying the exact conservation laws in finite precision computation/finite precision physics in which by necessity local mean values will
    be taken, which is the essence of turbulence. This also gives a way to understand turbulence as shown in my book Computational Turbulent Incompressible Flow. To simply assume positive dissipation/friction without explaining from where the dissipation/friction is coming, does not answer the key question why there is a 2nd law and why there is dissipation/friction. This is what I seek to do. It can be viewed as a very primitive form of statistics without the drawbacks of statistical mechanics with its horrendous calculations of number of microstates. The irreversibility of smashing an egg is then explained as an impossibility to realize the high precision required in finite time.

  9. So you do acknowledge that statistics is unavoidable?

    Further, there seems to be a lot of unproven assumptions and loose ends. Have you tried this approach on nano-systems? Does it work if this is applied to all the empirical data connected to nano-science?

  10. Claes, I do not disagree with your assessment. The reason I pointed to Lubos's post was that he clearly determines using statistics that heat flows one way as does time and DLR can not occur in the macrostate if the atmospheric temperature is less than the surface temperature because in his terms that would decrease entropy.
    I find Lubos's string theory interesting. I think he is very knowledgeable in his field but I recognise that he has no experience in engineering science such as heat & mass transfer, or fluid dynamics. For example he makes some incorrect assumption in his post about Venus, http://motls.blogspot.com.au/2010/05/hyperventilating-on-venus.html, but a least he comes up with the answer that there is no significant "greenhouse effect" on Venus. His post and others have discredited the gurus of AGW such as Sir John Houghton (who included a greenhouse Venus in his poor quality book "The Physics of Atmospheres 1986 2nd edition)

  11. No, it is snot tatistics but finite precision computation, which is like chopping decimals up or down, which is a very primitive and hence understandable form of statistics, very different from counting number of microstates. Finite precision computation gives classical deterministic models a new life to the benefit of mankind. Applications are endless.

  12. In my view statistics is not real objective physics but rather subjective physics of the mind of the observer, which at least for macroscopic physics is against the basic principle of science of objectivity and repeatability.

  13. If you come to rhe same result, as Boltzmann and Planck, with your finite precision computation methode, what´s then the problem. That´s very good I think. The result is even more true the more ways you can prove it in. But with your way to calculate things, you can never proove the nonexistance of DLR, how much you will try. Planck`s law tells it exist and furthermore Kirchoffs radiation law tells that DLR can be absorbed by materia at the surface of the earth. If you say something else, you are denying these laws. Are you?

  14. DLR violates the 2nd law, and thus cannot exist as a physical phenomenon, only as a phantasm in twisted minds.

  15. Then Planck´s and Kirchoff´s radiation laws violates the 2nd law! Do you really believe that?

  16. DLR violates the 2nd Law. If Planck was alive he could tell if he insists that his radiation law includes DLR. In his absence we have to think ourselves, and this is what I have done.

  17. Claes,

    you write: "DLR violates the 2nd Law."

    Why? DLR is a consequence of the temperature of the atmosphere.
    So why is it violating the 2nd law?

    Can you explain this without repeating just your claim.

    Best regards

  18. Transfer of heat energy from cold to warm without external forcing violates the 2nd law.

  19. (I repeat:)
    CO2 (in atmosphere) radiates at 667. Also, acc to Planck´s law, the earth radiation spectrum contains 667. Then Kirchoff´s law tells that the earth can absorb this radiation. Do you deny this?

  20. I repeat: If you are convinced that non-forced heat transfer from cold to warm is possible, I suggest that you present your ideas to Vattenfall and study the reaction, instead of bombarding me with silly questions.

  21. Claes, I don´t say that heat is transferred from CO2 to the earth. I just say that, in the first step, radiation from CO2 evidently, acc to Planck´s and Kirchoff´s laws, is absorbed by the earth. In the next step, of course, the earth is reemitting this energy, or more, back to some receiver, acc to the same laws. This means that the earth can´t be directly warmed by a colder materia, like CO2, but DLR from a colder body exists. Is this so hard to understand. This also means that the 2nd law is not applicable in the first step above, but after the second step. The 2nd law is best suited for macroscopic systems. It was invented before the atomic behaviour was fully clear.
    I don´t think my view on things is more silly than yours, rather the opposite. Can you agree on something I have written here.

  22. Lasse H, it seems you do not want to understand or open your closed thinking. I have suggested to you to read chapter 4-Thermodynamics and 5-Heat& Mass transfer of Perry's Chemical Engineering Handbook which has been in existence since 1934 with many revisions and editions to keep it upto date. Mark's Mechanical Engineering Handbook has similar sections but less detailed about the work of Prof Hoyt Hottel who carried out a vast amount of research on the absorption and emission of gases (from combustion) containing water vapor and carbon dioxide. Clearly you do not understand Kirchoff's law, or radiative & convective heat transfer (are you aware of the Nusselt number?- I think not). What you say above is wrong. You are just repeating the nonsense spread by alarmists who a) have no qualifications in engineering science and b) have had no experience of design and measurement of combustion and heat transfer systems and equipment.

  23. Cementafriend: Planck´s and Kirchoff´s laws speak for themselves. I have not invented them.

  24. The Uranus Dilemma

    Consideration of the planet Uranus very clearly indicates that radiative models (and any type of "Energy Budget" similar to those produced by the IPCC) can never be used to explain observed temperatures on Uranus. We can deduce that there must be some other physical process which transfers some of the energy absorbed in the upper levels of the Uranus atmosphere from the meagre 3W/m^2 of Solar radiation down into its depths, and that same mechanism must "work" on all planets with significant atmospheres.

    Uranus is an unusual planet in that there is no evidence of any internal heat generation. Yet, as we read in this Wikipedia article, the temperature at the base of its (theoretical) troposphere is about 320K - quite a hot day on Earth. But it gets hotter still as we go further down in an atmosphere that is nearly 20,000Km in depth. Somewhere down there it is thought that there is indeed a solid core with about half the mass of Earth. The surface of that mini Earth is literally thousands of degrees. And of course there's no Solar radiation reaching anywhere near that depth.

    So how does the necessary energy get down there, or even as far as the 320K base of the troposphere? An explanation of this requires an understanding of the spontaneous process described in the Second Law of Thermodynamics, which is stated here as ...

    "The second law of thermodynamics: An isolated system, if not already in its state of thermodynamic equilibrium, spontaneously evolves towards it. Thermodynamic equilibrium has the greatest entropy amongst the states accessible to the system"

    Think about it, and I'll be happy to answer any questions - and explain what actually happens, not only on Uranus, Venus, Jupiter etc, but also on Earth.