Timeline for Where does a math person go to learn statistical mechanics?
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| Mar 28, 2014 at 7:58 | comment | added | Yvan Velenik | Notice also that LD theory provides mostly structural information: it allows you, for example, to relate rate functions (thermodynamic potentials) corresponding to different ensembles. However, by itself, it generally tells you basically nothing about these rate functions, or their minimizers (not even about uniqueness or not of the latter, i.e., the issue of phase transitions; to obtain such information, you have usually to go far beyond LD theory). | |
| Mar 24, 2014 at 8:27 | comment | added | Yvan Velenik | Of course, LD theory is a very important piece of the toolbox of the statistical physicist, both conceptually and practically. I just think that one should not overstate its role. | |
| Mar 24, 2014 at 8:25 | comment | added | Yvan Velenik | As for explicit examples, I doubt that LD theory helps much if you want to determine, say, critical exponents, asymptotic behavior of correlation functions, etc. | |
| Mar 24, 2014 at 8:23 | comment | added | Yvan Velenik | Well, large deviations theory is about logarithmic asymptotics of various probabilities, which only corresponds to a tiny piece of the statistical physics domain. Even keeping with the most probabilistic aspects of statistical physics, you can say that the latter is interested in studying properties of Gibbs measures. Many of these properties cannot be cast in a large deviations framework (just as large deviations theory only highlights some aspects of probability theory). | |
| Mar 24, 2014 at 2:25 | comment | added | tortortor | @YvanVelenik: you may well be right, I am an amateur on this topic. Could you give an example or a sketch of the difference? | |
| Mar 23, 2014 at 11:36 | comment | added | Yvan Velenik | Although large deviations theory is certainly deeply related to important aspects of statistical mechanics (the probabilistic interpretation of thermodynamic potentials, the equivalence of ensembles, the variational principle, etc.), the latter certainly does not reduce to the former. | |
| S Feb 18, 2014 at 17:32 | history | answered | tortortor | CC BY-SA 3.0 | |
| S Feb 18, 2014 at 17:32 | history | made wiki | Post Made Community Wiki by tortortor |