Trajectory branching in Liouville space as the source of irreversibility
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From: Han de Bruijn on 1 Jun 2010 07:15 On May 31, 4:58 pm, "Juan R." González-Álvarez <nowh...(a)canonicalscience.com> wrote: > TRAJECTORY BRANCHING IN LIOUVILLE SPACE AS THE SOURCE OF IRREVERSIBILITY [ .. snip .. ] Believe me: your theory is COMPLETELY IRRELEVANT. Since you've ignored a previous posting of mine about the subject, I'll post it here again. http://groups.google.nl/group/sci.math/msg/795fa069678b2182 So after failure has become evident, you cannot say that nobody ringed an alarm bell. Or didn't issue an alternative. If Numerical Approximations of physical phenomena are to be considered as a fundamental tip hint, then the following is a relevant reference. And it is SIMPLE and straightforard mathematics. Contrary to yours. http://hdebruijn.soo.dto.tudelft.nl/jaar2004/purified.pdf In this article it is demonstrated that the Numerical Approximation of convection (and diffusion) in fluid flow IS irreversible from the very start. This has been known for a long time: as the need for "_UPWIND_" schemes in finite volume contexts. The article _generalizes_ this idea for ALL (unified) numerical approximations. Or rather: the _numerical_ formulations ARE the proper laws of nature. Common calculus is only an "approximation" of the general(ized) numerical law which is considered as "exact" and it is irreversible from the very start. In order to see this, replace the (u.d/dx + v.d/dy) operator by (d/dt). So the upwind scheme, which is irreversible, applies to the latter (= time) as well. Once you've seen it, it's very easy. And quite elegant: http://www.xs4all.nl/~westy31/Electric.html#Irregular Han de Bruijn
From: "Juan R." González-Álvarez on 1 Jun 2010 12:31 Han de Bruijn wrote on Tue, 01 Jun 2010 04:15:09 -0700: > On May 31, 4:58 pm, "Juan R." González-Álvarez > <nowh...(a)canonicalscience.com> wrote: > >> TRAJECTORY BRANCHING IN LIOUVILLE SPACE AS THE SOURCE OF >> IRREVERSIBILITY > > [ .. snip .. ] > > Believe me: your theory is COMPLETELY IRRELEVANT. Since you've ignored a > previous posting of mine about the subject, I'll post it here again. Sorry, I believed that it was some kind of mathematicians joke, but now I see that you pretend to be serious :-D (...) > If Numerical Approximations of physical phenomena are to be considered > as a fundamental tip hint, then the following is a relevant reference. > And it is SIMPLE and straightforard mathematics. Contrary to yours. > > http://hdebruijn.soo.dto.tudelft.nl/jaar2004/purified.pdf This is an completely irrelevant reference for the goal of obtaining a *grand* theory of irreversibility. It would be needed to apply about a dozen of approximations to the general theory described in the OP before deriving the simplistic equations (e.g. the diffusion equations in page 4) that you are using. Our goal is to explain Nature and its complexity, which includes the obtaining of equations for explaining phenomena beyond the limits of the approximated equations at your starting point. There is also some wrong statements in that work. For instance, your claim that a flow of heat from a low temperature region to a high temperature region violates the Second law of thermodynamics is not all right. It was showed several years ago that a flow of that kind is compatible with the second law, when the truncated (approximated) equations for heat transport are substituted by their generalized cousins. The generalized expressions are very useful for nanotechnology and molecular biology. The links to the relevant works were already given in the *other* thread. > In this article it is demonstrated that the Numerical Approximation of > convection (and diffusion) in fluid flow IS irreversible from the very > start. This has been known for a long time Yes, a numerical approximation to an irreversible equation is... irreversible. Congrats if you got this result by yourself :-D -- http://www.canonicalscience.org/ BLOG: http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html
From: Han de Bruijn on 2 Jun 2010 07:33 On Jun 1, 6:31 pm, "Juan R." González-Álvarez <nowh...(a)canonicalscience.com> wrote: > Han de Bruijn wrote on Tue, 01 Jun 2010 04:15:09 -0700: > > > On May 31, 4:58 pm, "Juan R." González-Álvarez > > <nowh...(a)canonicalscience.com> wrote: > > >> TRAJECTORY BRANCHING IN LIOUVILLE SPACE AS THE SOURCE OF > >> IRREVERSIBILITY > > > [ .. snip .. ] > > > Believe me: your theory is COMPLETELY IRRELEVANT. Since you've ignored a > > previous posting of mine about the subject, I'll post it here again. > > Sorry, I believed that it was some kind of mathematicians joke, but now > I see that you pretend to be serious :-D > > (...) > > > If Numerical Approximations of physical phenomena are to be considered > > as a fundamental tip hint, then the following is a relevant reference. > > And it is SIMPLE and straightforard mathematics. Contrary to yours. > > >http://hdebruijn.soo.dto.tudelft.nl/jaar2004/purified.pdf > > This is an completely irrelevant reference for the goal of obtaining a > *grand* theory of irreversibility. There IS NO *grand* theory of irreversibility. And there NEVER will be one of the kind. The Ultimate Arrogance of Physics all over the place. > It would be needed to apply about a dozen of approximations to the general > theory described in the OP before deriving the simplistic equations > (e.g. the diffusion equations in page 4) that you are using. Not "the diffusion equations" but the CONVECTION part of the equations is relevant. (The article handles convection _and_ diffusion, BTW, for some other, more mundane purposes. It's not meant as a *grand* theory, of course). > Our goal is to explain Nature and its complexity, which includes the > obtaining of equations for explaining phenomena beyond the limits of the > approximated equations at your starting point. It's the other way around, as I've said. > There is also some wrong statements in that work. For instance, > your claim that a flow of heat from a low temperature region to a high > temperature region violates the Second law of thermodynamics is not all right. The context of the article is clearly classical _macroscopic_ physics. And my claim is obviously correct in that realm. > It was showed several years ago that a flow of that kind is compatible > with the second law, when the truncated (approximated) equations for heat > transport are substituted by their generalized cousins. > > The generalized expressions are very useful for nanotechnology and molecular > biology. That is microscopic physics. And the second law of theormodynamics has never been established for that realm, indeed. > The links to the relevant works were already given in the *other* thread. > > > In this article it is demonstrated that the Numerical Approximation of > > convection (and diffusion) in fluid flow IS irreversible from the very > > start. This has been known for a long time > > Yes, a numerical approximation to an irreversible equation > is... irreversible. Oh no, I've proved that ANY numerical approximation to a _reversible_ equation - namely pure convection - is ALWAYS irreversible. And that must come as a surprise, even for you. > Congrats if you got this result by yourself :-D I stand on the shoulders of those who invented 'UPWIND'. Thank you. > --http://www.canonicalscience.org/ > > BLOG:http://www.canonicalscience.org/publications/canonicalsciencetoday/ca... Han de Bruijn
From: "Juan R." González-Álvarez on 3 Jun 2010 11:42 Han de Bruijn wrote on Wed, 02 Jun 2010 04:33:26 -0700: > On Jun 1, 6:31 pm, "Juan R." González-Álvarez > <nowh...(a)canonicalscience.com> wrote: > >> Han de Bruijn wrote on Tue, 01 Jun 2010 04:15:09 -0700: >> >> > On May 31, 4:58 pm, "Juan R." González-Álvarez >> > <nowh...(a)canonicalscience.com> wrote: >> >> >> TRAJECTORY BRANCHING IN LIOUVILLE SPACE AS THE SOURCE OF >> >> IRREVERSIBILITY >> >> > [ .. snip .. ] >> >> > Believe me: your theory is COMPLETELY IRRELEVANT. Since you've >> > ignored a previous posting of mine about the subject, I'll post it >> > here again. >> >> Sorry, I believed that it was some kind of mathematicians joke, but now >> I see that you pretend to be serious :-D >> >> (...) >> >> > If Numerical Approximations of physical phenomena are to be >> > considered as a fundamental tip hint, then the following is a >> > relevant reference. And it is SIMPLE and straightforard mathematics. >> > Contrary to yours. >> >> >http://hdebruijn.soo.dto.tudelft.nl/jaar2004/purified.pdf >> >> This is an completely irrelevant reference for the goal of obtaining a >> *grand* theory of irreversibility. > > There IS NO *grand* theory of irreversibility. And there NEVER will be > one of the kind. The Ultimate Arrogance of Physics all over the place. If you read the first message you would see that I argue why cannot exist an "ultimate theory" (as arrogant but misinformed physicists claim). You confound that with a "grand theory" which is already at hand. >> It would be needed to apply about a dozen of approximations to the >> general theory described in the OP before deriving the simplistic >> equations (e.g. the diffusion equations in page 4) that you are using. > > Not "the diffusion equations" but the CONVECTION part of the equations > is relevant. (The article handles convection _and_ diffusion, BTW, for > some other, more mundane purposes. It's not meant as a *grand* theory, > of course). I was refering to the diffusion equations that *you* give in the page 4 when *you* write "analysis of Diffusion", "in case of pure diffusion", etc. I was referening to those approx. equations therein. Moreover, you seem to be confounding the modern usage of the terms convention and advenction. Many people uses the term convention as including both advenction and diffusion. I.e. they treat diffusion as a subclass of convention. In any case, this are only conventions and naming. The IMPORTANT point is that everything in your equations is highly approximated and limited in scope, and thus *irrelevant* when studing more general experimental situations. (...) >> There is also some wrong statements in that work. For instance, your >> claim that a flow of heat from a low temperature region to a high >> temperature region violates the Second law of thermodynamics is not all >> right. > > The context of the article is clearly classical _macroscopic_ physics. > And my claim is obviously correct in that realm. Yours continues being wrong because the modifications to the equations are compatible with the Second law in the same domain. Moreover, the flow from low to hot regions is also permitted above the micro and nano-scale. It can happen for systems with N >> 10^23. Others and me already wrote about that. The relevant literature was already cited. (...) >> > In this article it is demonstrated that the Numerical Approximation >> > of convection (and diffusion) in fluid flow IS irreversible from the >> > very start. This has been known for a long time >> >> Yes, a numerical approximation to an irreversible equation is... >> irreversible. > > Oh no, I've proved that ANY numerical approximation to a _reversible_ > equation - namely pure convection - is ALWAYS irreversible. And that > must come as a surprise, even for you. Sorry, but it is not a surprise. I have read so bogus claims for several years now. It always happen that those people uses what van Kampen correctly named "mathematical funambulism". When the numerical approximation to a reversible equation is CORRECTLY done the result is reversible. As said before I plan to write a future report analizing some of those mathematical funambulisms. It is not my aim to write an enciclopedia of the nonsense nor to review any wrong article by any author, but merely to analize some very common misunderstandings and mathematical fallacies that one reads in the typical literature too often. -- http://www.canonicalscience.org/ BLOG: http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html
From: Han de Bruijn on 5 Jun 2010 06:24
On 3 jun, 17:42, "Juan R." González-Álvarez <nowh...(a)canonicalscience.com> wrote: > Han de Bruijn wrote on Wed, 02 Jun 2010 04:33:26 -0700: > > On Jun 1, 6:31 pm, "Juan R." González-Álvarez > > <nowh...(a)canonicalscience.com> wrote: > > >> Han de Bruijn wrote on Tue, 01 Jun 2010 04:15:09 -0700: > > >> > On May 31, 4:58 pm, "Juan R." González-Álvarez > >> > <nowh...(a)canonicalscience.com> wrote: > > >> >> TRAJECTORY BRANCHING IN LIOUVILLE SPACE AS THE SOURCE OF > >> >> IRREVERSIBILITY > > >> > [ .. snip .. ] > > >> > Believe me: your theory is COMPLETELY IRRELEVANT. Since you've > >> > ignored a previous posting of mine about the subject, I'll post it > >> > here again. > > >> Sorry, I believed that it was some kind of mathematicians joke, but now > >> I see that you pretend to be serious :-D > > >> (...) > > >> > If Numerical Approximations of physical phenomena are to be > >> > considered as a fundamental tip hint, then the following is a > >> > relevant reference. And it is SIMPLE and straightforard mathematics. > >> > Contrary to yours. > > >> >http://hdebruijn.soo.dto.tudelft.nl/jaar2004/purified.pdf > > >> This is an completely irrelevant reference for the goal of obtaining a > >> *grand* theory of irreversibility. > > > There IS NO *grand* theory of irreversibility. And there NEVER will be > > one of the kind. The Ultimate Arrogance of Physics all over the place. > > If you read the first message you would see that I argue why cannot > exist an "ultimate theory" (as arrogant but misinformed physicists claim).. > You confound that with a "grand theory" which is already at hand. ?? > >> It would be needed to apply about a dozen of approximations to the > >> general theory described in the OP before deriving the simplistic > >> equations (e.g. the diffusion equations in page 4) that you are using. > > > Not "the diffusion equations" but the CONVECTION part of the equations > > is relevant. (The article handles convection _and_ diffusion, BTW, for > > some other, more mundane purposes. It's not meant as a *grand* theory, > > of course). > > I was refering to the diffusion equations that *you* give in the page 4 > when *you* write "analysis of Diffusion", "in case of pure diffusion", etc. > I was referening to those approx. equations therein. > > Moreover, you seem to be confounding the modern usage of the terms > convention and advenction. Many people uses the term convention as including > both advenction and diffusion. I.e. they treat diffusion as a subclass of convention. The fact alone that you cannot even spell the words "convection" and "advection" correctly is enough evidence: that Numerical Analysis is not your territory. And no, diffusion is definitely NOT a subclass of convection. But I agree that many people are incompetent. > In any case, this are only conventions and naming. The IMPORTANT point is that everything > in your equations is highly approximated and limited in scope, and thus *irrelevant* > when studing more general experimental situations. I see now that my article indeed is too much off-topic with respect to the subject of this thread to be convincing. Therefore I've decided to start up another of my free projects. And devise a writeup which _is_ entirely devoted to Time Reversal. As soon as I find time. > (...) > > >> There is also some wrong statements in that work. For instance, your > >> claim that a flow of heat from a low temperature region to a high > >> temperature region violates the Second law of thermodynamics is not all > >> right. > > > The context of the article is clearly classical _macroscopic_ physics. > > And my claim is obviously correct in that realm. > > Yours continues being wrong because the modifications to the equations are > compatible with the Second law in the same domain. Moreover, the flow > from low to hot regions is also permitted above the micro and nano-scale. It can happen > for systems with N >> 10^23. Others and me already wrote about that. The relevant literature was already cited. In your SF literature maybe yes. But not in my world. > (...) > > >> > In this article it is demonstrated that the Numerical Approximation > >> > of convection (and diffusion) in fluid flow IS irreversible from the > >> > very start. This has been known for a long time > > >> Yes, a numerical approximation to an irreversible equation is... > >> irreversible. > > > Oh no, I've proved that ANY numerical approximation to a _reversible_ > > equation - namely pure convection - is ALWAYS irreversible. And that > > must come as a surprise, even for you. > > Sorry, but it is not a surprise. I have read so bogus claims for several > years now. It always happen that those people uses what van Kampen correctly > named "mathematical funambulism". When the numerical approximation to a reversible > equation is CORRECTLY done the result is reversible. Nonsense, nonsense and nonsense. And there are sooo many little names. > As said before I plan to write a future report analizing some of those > mathematical funambulisms. It is not my aim to write an enciclopedia of the > nonsense nor to review any wrong article by any author, but merely to analize > some very common misunderstandings and mathematical fallacies that one reads > in the typical literature too often. I'm breathlessly awaiting. > --http://www.canonicalscience.org/ > > BLOG:http://www.canonicalscience.org/publications/canonicalsciencetoday/ca...- Thank you for triggering me to start that new project, anyway. Han de Bruijn |