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| bio | website | unige.ch/math/folks/velenik |
|---|---|---|
| location | Geneva, Switzerland | |
| age | 43 | |
| visits | member for | 1 year, 1 month |
| seen | 17 mins ago | |
| stats | profile views | 100 |
Professor at the Mathematics department of the University of Geneva. Mostly working at the intersection of probability theory and statistical physics.
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Oct 6 |
comment |
Open boundary condition and Glauber Dynamics The choice of boundary conditions plays a crucial role in the phase coexistence regime. You should have a look at Martinelli's lecture notes, which are available at imap.ma.utexas.edu/mp_arc/c/97/97-578.ps.gz . There are, of course, more recent works, in particular concerning higher-dimensional systems. |
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Aug 19 |
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Loschmidt's paradox - really a paradox? No, the resolution of this "paradox" has nothing to do with the H-theorem. See the refs in my comment above. |
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Jul 11 |
awarded | Revival |
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Jun 29 |
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Loschmidt's paradox - really a paradox? No, it is considered irrelevant today. See, e.g., this paper. Of course, this does not imply that the problem of the foundations of statistical physics has been settled (in particular, the proper interpretation of probabilities in the theory). |
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Jun 22 |
revised |
What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis? Added one relevant reference and updated another link (which didn't work anymore)... |
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Jun 22 |
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Recommendations for Statistical Mechanics book Just in case. Here are the google book pages for the last 2 refs, so that you can have an idea of what is done there and at which level: Ruelle, Georgii. |
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Jun 21 |
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Recommendations for Statistical Mechanics book Another good (but probably too advanced) book is the "old" book by Ruelle, "Statistical Mechanics - Rigorous Results". If you have the level in maths, and are interested in the mathematical theory of phase transitions for lattice systems, the classical reference is Georgii's "Gibbs measures and phase transitions" (although that's more graduate level stuff). |
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Jun 21 |
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Recommendations for Statistical Mechanics book A good advanced book that covers in details and with mathematical rigor what you want and much more is Gallavotti's "Statistical Mechanics - a short treatise", which is not so short actually... You can get it from here. |
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Jun 12 |
awarded | Enthusiast |
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Jun 5 |
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proving that the free energy is extensive For a much more detailed argument, see the beautiful paper by Jaynes: bayes.wustl.edu/etj/articles/gibbs.paradox.pdf . |
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Jun 5 |
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proving that the free energy is extensive No, undistinguishability of particles has nothing to do with that. The point is that the thermodynamical definition of entropy is given up to an arbitrary function of the number of particles (it is defined using a differential relation, with fixed number of particles). So the same is true when you define the entropy in stat. mech., since this is done by analogy with the thermodynamic one (they satisfy the thermodynamic relations). The only reason why you need an N! (or something like $N^N$) is that you want entropy to be extensive. This is an additional assumption, which does not always hold. |
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Jun 5 |
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Lacking of scale and distribution moments @LubošMotl: of course it's a matter of definitions, but there is at least one good, pragmatic reason to say that the Cauchy distribution does not have an expectation: an iid sequence of such random variables will not satisfy the law of large numbers (the sample mean is again Cauchy-distributed)... |
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Jun 1 |
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What is known about some massive Gaussian models on a lattice? BTW, if you'd like more informations, or additional references, etc., you should rather contact me by email (the address is indicated on my homepage). |
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Jun 1 |
awarded | Editor |
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Jun 1 |
revised |
What is known about some massive Gaussian models on a lattice? added 92 characters in body |
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May 31 |
answered | What is known about some massive Gaussian models on a lattice? |
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May 28 |
awarded | Supporter |
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May 25 |
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Surface tension of solutions and mixtures If you want some pointers to some of the information about that topic that can be rigorously extracted in simple Ising-like systems, you can have a look at scholarpedia.org/article/Interface_free_energy . Of course, much more is known (in these "simple" models). |
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May 4 |
awarded | Nice Question |
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May 4 |
awarded | Nice Answer |
