Timeline for Why do many people link entropy to chaos?
Current License: CC BY-SA 4.0
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| Nov 24, 2018 at 19:39 | history | edited | Wrzlprmft | CC BY-SA 4.0 |
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| Jun 25, 2016 at 8:06 | comment | added | Wrzlprmft | @Malkoun: […] recommend something to read containing the definitions of all these dynamical systems words. – I just stumbled upon these notes, which defines almost all those terms. However, be careful about the fourth part (“and yet more”), which, while technically correct, does not issue appropriate warnings against conflating similarly named concepts (such as molecular chaos and chaos). Also, the notion that all chaotic systems are ergodic is wrong, e.g., there are very simple chaotic systems that are weak ergodicity breaking. | |
| Jun 25, 2016 at 7:44 | comment | added | Malkoun | Ok, I understand. I apologize for misquoting you (I deleted that previous comment). | |
| Jun 25, 2016 at 7:41 | comment | added | Wrzlprmft | In your classification, you seem to rule out the existence of high-dimensional regular dynamics. Is that a well-known fact? – I do not dispute the existence of high-dimensional regular dynamics (in fact, I encounter such systems in my research); I rule out the existence of regular, realistic many-particle dynamics (with some temperature). This should be impossible to validate in experiment or model, as we cannot distinguish a high-dimensional quasiperiodic dynamics from a chaotic one. However, as quasiperiodic dynamics are quite special, I argue that they should not prevail in reality. | |
| Jun 25, 2016 at 7:36 | comment | added | Malkoun | I think what you are arguing for, is that chaotic and ergodic are two different properties of a system, am I right in interpreting your argument? Anyway, I am just learning about all this terminology. I would like to ask you, or someone else, to possibly recommend something to read containing the definitions of all these dynamical systems words. Any suggestion for a nice dynamical systems book, or online notes, or paper? I would like to see the words: regular, chaotic and ergodic, all clearly defined please. | |
| Jun 25, 2016 at 7:27 | history | edited | Wrzlprmft | CC BY-SA 3.0 |
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| Jun 25, 2016 at 6:40 | comment | added | Wrzlprmft | I did not understand everything in your answer (my background is not in Physics) – Can you elaborate what you did not understand, so I can improve my explanation? — that the link with chaos is more like a theorem – I never saw it formulated as such and I do not think that it would have any useful applications. Chaos theory and statistical mechanics tend to look at vastly different systems and vastly different aspects of systems. Also, keep in mind that almost every real system features entropy and almost every real system features chaos. | |
| Jun 25, 2016 at 5:56 | comment | added | Malkoun | I did not understand everything in your answer (my background is not in Physics), but I have come to think that the definition of entropy itself, say in Statistical Mechanics, is along the lines of microscopic freedom, as Christoph mentioned above, and that the link with chaos is more like a theorem, which does not hold for all systems, but it seems to hold for a big nice special class of systems. This of course brings up many interesting questions (which may be the subject of another post I suppose). | |
| Jun 24, 2016 at 19:16 | history | answered | Wrzlprmft | CC BY-SA 3.0 |