1,489 reputation
416
bio website unige.ch/math/folks/velenik
location Geneva, Switzerland
age 44
visits member for 1 years, 11 months
seen 1 hour ago

Professor at the Mathematics department of the University of Geneva. Mostly working at the intersection of probability theory and statistical physics.


May
9
comment What is the interface tension between ordered and disordered phases of the Potts model?
I just realized that, in the title of your question, you are asking for the surface tension between the ordered and disordered states. The lack of symmetry between these two phases makes the definition slightly more involved than in the Ising case (or between 2 ordered Potts phases). Nevertheless, the idea remains completely similar, and you should first understand the definition in the link I have given. I can give you a more detailed explanation when symmetry is absent next week (I am at a conference right now...).
May
7
comment What is the interface tension between ordered and disordered phases of the Potts model?
The surface tension is defined as the surface-order contribution (per unit area) to the free energy coming from the presence of an interface between two phases. See scholarpedia.org/article/Interface_free_energy for example for a precise definition (in the Ising case, but the Potts case is essentially identical).
Apr
26
awarded  Yearling
Apr
23
comment Why does the Boltzmann factor $e^{-E/kT}$ seem to imply that lower energies are more likely?
No, the Boltzmann distribution is used for systems in contact with a reservoir, so the energy is not conserved. (Or, equivalently, for a finite subsystem of an isolated system; but in that case too, the Boltzmann factor takes into account the energy of the full subsystem and provides the probability density on the phase space of the subsystem.)
Apr
23
comment Why does the Boltzmann factor $e^{-E/kT}$ seem to imply that lower energies are more likely?
I don't think that restricting the Boltzmann factor to a specific degree of freedom is standard terminology (I just checked several books to see whether I had been misusing the term for years). The Boltzmann factor is usually seen as (say, in the classical case) the function $e^{-H/kT}$ on the phase space (where $H$ is the Hamiltonian of the system). It does provide the (unnormalized) probability density associated to the whole system.
Apr
16
awarded  Good Answer
Apr
9
comment Why there is no “Edison” unit in physics?
@Voitcus: This is not correct. His was the first able to play back a sound it previously recorded. The first sound recorder seems to be the Phonautograph, patented in 1857 by Édouard-Léon Scott de Martinville. Some of his recordings were played back in 2008. You can look it up, e.g., in wikipedia.
Apr
8
comment Does entropy really always increase (or stay the same)?
A nice discussion can be found at scholarpedia.org/article/… .
Mar
31
comment Is there a mechanism for time symmetry breaking?
You should read scholarpedia.org/article/… .
Mar
20
comment Results of Statistical Mechanics first obtained by formal mathematical methods
Actually, the opinion of XIXth Century physicists concerning the atomic theory is much more subtle than that. Interested people should read, e.g., the very nice books by Brush (The kind of motion we call heat, 2 volumes) and Cercignani (Ludwig Boltzmann:The Man Who Trusted Atoms).
Mar
20
revised Determining the probability of a particular site having a particular spin in an Ising model
More precise
Mar
19
answered Determining the probability of a particular site having a particular spin in an Ising model
Mar
9
comment Difference between theoretical physics and mathematical physics?
@PeterShor: Yes, that's right, although, there is usually a temporal shift: topics studied by mathematical physicists have often been considered well understood for years by theoretical physicists ;) .
Mar
8
answered Difference between theoretical physics and mathematical physics?
Mar
8
comment Difference between theoretical physics and mathematical physics?
The approaches are also very different. Theoretical physicists are much more pragmatic, and consequently allow themselves all kind of uncontrolled approximations, mathematically meaningless operations, etc. In mathematical physics, once the problem is posed, the derivation is supposed to be purely deductive, without any additional, implicit assumption.
Mar
8
comment Difference between theoretical physics and mathematical physics?
Mathematical physics and theoretical physics are absolutely not the same disciplines. Just browse a random issue of Communications in Mathematical Physics! Mathematical Physics is bona fide mathematics, but applied to physics questions: the papers have the traditional Lemma/Proposition/Theorem structure of mathematics papers. Compare with the typical paper in theoretical physics. And it's not just a matter of style: papers in mathematical physics often could just as well be published in mathematics journals, which is not the case for almost all papers in theoretical physics.
Mar
4
comment Is there a formal definition of a macroscopic variable in statistical mechanics?
@Stereotomy: Yes, in finite volumes there is no unique way of differentiating between macroscopic and microscopic observables. On the other hand, if you consider averages over sufficiently large regions (say, much beyond correlation length), then typical values will be sharply concentrated on the deterministic value of the corresponding infinite-volume observable, and you can even quantify the size and law of the (small) fluctuations. So, in this sense, this characterization of "macroscopic observable", even though it is obviously a mathematical idealization, is relevant for finite systems.
Mar
4
comment Is there a formal definition of a macroscopic variable in statistical mechanics?
@Stereotomy: Well, there is no general recipe, which is one of the reasons it is so convenient to work with infinite systems. But, for both examples I gave, it is quite obvious how you would construct finite-volume analogues: the first one would just be the average over all the (finitely many) spins in the system; the second might be (say, in a cubic system of sidelength $L$) something like "there are no connected components of diameter larger than $\epsilon L$ for example. Again, things become fuzzy as soon as you work with finite systems, obviously.
Mar
4
comment Is there a formal definition of a macroscopic variable in statistical mechanics?
[cont.] and that macroscopic observables take constant values. Both things are only formally true for infinite systems. Of course, they "almost" hold for large finite systems.
Mar
4
comment Is there a formal definition of a macroscopic variable in statistical mechanics?
@Nathaniel: Sure. Nevertheless, this is the notion that is used in this context. Of course, the infinite-volume claims that you can extract for such observables do have finite-volume counterparts (that you can rigorously derive) for their finite-volume, physically more directly relevant, versions. But, again, you lose the possibility of having clear-cut definitions. Note also that if you're interested in deriving thermodynamical properties of the system, then these approximations are very natural: in thermodynamics, one usually assumes that the shape of the sample is irrelevant [to be cont.]