Hello, Nanite, and welcome to Wikipedia! I would give you the usual welcome spiel but it looks like you've got just about everything figured out. The diagrams in particular look very nice; I usually use Inkscape but its formula support is pretty bad -- I guess I should check out lpe. Keep up the good work and let me know if you have any questions. Cheers, a13ean (talk) 21:47, 3 June 2013 (UTC)[reply]

Yes, Ipe is my favourite. I have to admit it's a bit awkward to work with at times due to partial gui support, but if you like LaTeX then you can get along with its idiosyncrasies. :) --Nanite (talk) 21:54, 3 June 2013 (UTC)[reply]

What is your source for the derivation in the section Derivation starting with grand canonical ensemble, i.e. the part beginning with "Due to the non-interacting quality...", and ending with "...and thus gives the exact Fermi-Dirac distribution for the entire state of the system"? Regards, --Bob K31416 (talk) 01:39, 11 June 2013 (UTC)[reply]

I admit I didn't look it up and just derived it myself, as I thought it was a pretty straightforward derivation. I mainly wanted to clean up some of the mess on the page with the previously posted derivations. I looked around and I found some other instances of the grand canonical approach (e.g., the first section of chapter 6 of Statistical Mechanics by R. K. SRIVASTAVA, J. ASHOK[1])... I'll add that book as a citation. --Nanite (talk) 13:36, 11 June 2013 (UTC)[reply]

In the section Derivations starting with canonical distribution, what is your source for the statement, "The reason for the inaccuracy is that the total number of fermions is conserved in the canonical ensemble, which contradicts the implication in Fermi–Dirac statistics that each energy level is filled independently from the others (which would require the number of particles to be flexible)"? Regards, --Bob K31416 (talk) 15:57, 11 June 2013 (UTC)[reply]

Well, good point, perhaps it's not stated quite precisely enough. A better way to state it might be something like "By the equivalence of ensembles in the thermodynamic limit,[cite any statmech book for this equivalence principle] the canonical ensemble is guaranteed to yield the same distribution as the result above, in the limit of a large number of particles. Indeed, as shown in the below derivations, once one makes the approximation of a large particle number they arrive at the Fermi-Dirac distribution. For small particle number, however, the Fermi-Dirac statistics are not exactly derivable from the canonical ensemble." --Nanite (talk) 13:57, 12 June 2013 (UTC)[reply]

Note that the derivation using the grand canonical distribution, involves essentially the same approximation as the derivation using the canonical distribution, because that is how the grand canonical distribution was derived. See Eqs. 4.4 and 4.21 in Srivastava & Ashok, which use Taylor expansions only up to the linear terms. --Bob K31416 (talk) 23:48, 12 June 2013 (UTC)[reply]

Sort of yes and sort of no. It's true that to have continuous parameters of temperature and chemical potential we need a big reservoir to supply energy and particles, respectively. In that sense, both the canonical ensemble and grand canonical ensemble are thermodynamic-limit approximations because they invoke a reservoir. On the other hand, I can still use the canonical ensemble to describe the probability distribution for a tiny finite system with only two energy states (e.g., a spin-1/2 paramagnetic impurity). In the same way I'd want to use grand canonical ensemble for a tiny system where states of different particle number are accessible, like electrons in a small capacitor or in an ionizable molecule.

If I wanted to compute the statistics of a noninteracting fermion system with, say, only four available single-particle states, I'll still get exactly Fermi-Dirac statistics if I use GCE; alternatively I can use CE with a large particle reservoir attached, however that would essentially involve rederiving GCE along the way. What wouldn't work is to use the CE for the finite system alone (fixing the number of particles in the finite system). --Nanite (talk) 09:24, 13 June 2013 (UTC)[reply]

Seems like you didn't understand my last message. No matter. Per WP:V, any claim that the derivation using the grand canonical distribution is exact, and any implication resulting from that claim, such as that the derivation using the grand canonical distribution is more exact than the derivation using the canonical distribution, will be removed or rewritten because it is unsourced. --Bob K31416 (talk) 11:39, 13 June 2013 (UTC)[reply]

Well, google books isn't letting me look at that chapter of the Srivastava book, so I'll have to refer you to another one, Kershon Huang's "Statistical mechanics" (2nd edition, 1987). (One could possibly find an online copy of it by searching for Huang, K. Statistical mechanics djvu, but that might be illegal to obtain if you don't own a physical copy.). Anyhow, the grand canonical ensemble for sure does get derived with a large number approximation (for a total system composed of large reservoir plus subsystem), but that approximation is taken only for the reservoir (critically, equation 7.30 and 7.33 assume very large reservoir). Nothing is assumed for the subsystem. That's why the final result is the exact probability distribution for the state of the subsystem, whether the subsystem is very large or finite. Note that the canonical ensemble can only be derived using a very similar approximation for a large heat reservoir (the critical approximation is made in Huang's equation 7.3, regarding reservoir entropy). Again, it too applies for finite subsystems.

Given that the grand canonical ensemble gives the exact probability distribution for any system (small or large) which is in equilibrium for exchange of particles and energy with an ideal reservoir (reservoir with fixed chemical potential and temperature), the two-line quickie derivation of Fermi-Dirac statistics inherits that exactness. Anyway, go ahead and make the changes you want to make. --Nanite (talk) 14:28, 13 June 2013 (UTC)[reply]

Since the changes you made to the first paragraph of Fermi energy do not correspond to either textbook definitions or the IUPAC definition (see thread: WT:PHYSICS#Fermi energy), I would be grateful if you would now revert them. Jheald (talk) 09:12, 26 June 2013 (UTC)[reply]

You provided a reference to the statement: "if a voltmeter is attached to the junction, one simply measures zero" (Page 404 of Sah, Chih-Tang (1991). Fundamentals of Solid-State Electronics. World Scientific. ISBN 9810206372). However, that statement is wrong, and one simply DOES NOT measure zero there. I haven't had access to that reference but, with a p-n junction, there is an internal potential which is caused by the workfunction difference between the n-type and p-type semiconductors. This potential equals the built-in potential (which is typically about 0.7 volts for silicon at room temp). The built-in potential is explained in Wikipedia's article on "p–n junction" and I use that as a reference. Also, please see http://ecee.colorado.edu/~bart/book/book/chapter4/ch4_2.htm#4_2_3 . Also, I just measured the voltage of several p–n junctions myself using an actual modern digital voltmeter, and none is zero (thermocouple effects are cancelled due to the symmetry of the contact electrode materials used and constant temperature) and they are very close to the calculated voltages. So please eliminate that false statement or correct it accordingly. Thank you.

98.217.147.183 (talk) 18:37, 15 August 2013 (UTC)[reply]

Was your voltmeter in volts mode (applying zero current), or was it in diode mode (applying nonzero current)? I tried this test as well just now and I measure less than 1 mV (0 within error) on a silicon PN junction diode, using a modern digital multimeter in DC volts mode (the multimeter has an input impedance of around 10 Mohm, for what it is worth). Actually you can see even in the link you provided, that the applied voltage V_a is defined as the difference between Fermi levels, divided by charge q (Fig. 4.2.4). When V_a is zero (zero applied voltage, i.e., neither forward or reverse bias), the situation is that in Fig. 4.2.3: a junction in thermal equilibrium with zero current. If you insist to think about things in terms of Galvani potentials, remember that there are also built-in potentials at the metal-semiconductor and semiconductor-metal junctions around the diode. --Nanite (talk) 20:35, 15 August 2013 (UTC)[reply]

My voltmeter was in volts mode (applying zero current). Your problem with your test is that you used a voltmeter with an input impedance of only around 10 Mohm (a so called low cost multimeter). Either use a high impedance voltmeter or a larger size p-n junction, such as a large photodiode or a photoelectric cell. And yes, the diode would be performing work in our non-infinite impedance voltmeters (unless you have it at absolute zero) - (think Peltier, photovoltaic effects, etc.) The cooler and smaller the junction, the higher the voltmeter impedance needed to sense the built-in potential. Again, the potentials at the metal-semiconductor and semiconductor-metal junctions around our diodes were cancelled out due to the symmetry of the contact electrode materials used, and fairly the same constant temperature of the junctions. The statement: "if a voltmeter is attached to the junction, one simply measures zero" in the article is incorrect. The measurements are very close to the calculated voltages. So please eliminate that false statement or correct it accordingly. Thank you.

98.217.147.183 (talk) 11:57, 26 September 2013 (UTC)[reply]

If you read up on Seebeck effect you'll find that it only occurs where there are temperature differences (regardless of whether one of the temperatures is zero). That is a non-equilibrium situation, as is the case of the photovoltaic effect. If you are measuring a nonzero voltage with a voltmeter, then the part is out of equilibrium for some reason (input bias current of voltmeter, temperature differences, light shining on, etc.). Let me know which model of voltmeter you're using, and which kind of diode you're measuring, under what conditions, and we can figure this out.

By the way, the semiconductor-metal junctions in a pn diode are usually very unsymmetrical (but it doesn't matter for equilibrium: the Fermi level is constant throughout). I think it's worth pointing out Herbert Kroemer's rule: "If, in discussing a semiconductor problem, you cannot draw an Energy Band Diagram, this shows that you don't know what you are talking about." Try to draw a band diagram for the pn diode at equilibrium including metal leads and see whether you can make a different voltage - in any sense - between the metal leads. I've included my own. --Nanite (talk) 20:55, 26 September 2013 (UTC)[reply]

(edit conflict) Voltmeters have large but finite internal resistances. You can't measure the built-in potential of a diode with one. If you could, that would violate energy conservation since a diode would be performing work. a13ean (talk) 20:35, 15 August 2013 (UTC)[reply]

Yep, what Nanite said. The diode test mode flows a current -- you couldn't do this with a galvanometer-type voltmeter for example. a13ean (talk)

In Maxwell–Jüttner distribution, some concerns about adherence to standard Wikipedia conventions and standard conventions of TeX usage arise:

• I presume Maxwell is James Clerk Maxwell, but the article doesn't say so, and doesn't say who Jüttner is. Those should be mentioned.
• It is not correct to write mc². Rather, it should say mc². One italicizes variables, but not digits and not parentheses or the like. This is consistent with TeX and MathJax usage, and is codified in WP:MOSMATH. I fixed this.
• Although you've got Maxwell–Jüttner and Maxwell–Boltzmann with an en-dash, later you have Fermi-Dirac and Bose-Einstein with a hyphen rather than an en-dash. I corrected this.
• Don't write \mathrm{exp}. Instead, write \exp. (And similarly with \log, \sin, \arctan, \max, \det, etc.) Contrast these:

a\mathrm{exp}b yields

a\exp b yields

The second form automatically provides proper spacing; the first does not. I changed this.

Michael Hardy (talk) 13:36, 13 September 2013 (UTC)[reply]

Thanks for correcting the errors (I just copied the text from the MB distribution page and didn't pay much attention to the exact typesetting from the previous writers). --Nanite (talk) 13:44, 13 September 2013 (UTC)[reply]

Hi. Thank you for your recent edits. Wikipedia appreciates your help. We noticed though that when you edited Grand canonical ensemble, you added a link pointing to the disambiguation page Joint probability density function (check to confirm | fix with Dab solver). Such links are almost always unintended, since a disambiguation page is merely a list of "Did you mean..." article titles. Read the FAQ • Join us at the DPL WikiProject.

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Thanks for contributing the new article Thermal transpiration. However, one of Wikipedia's core policies is that material must be verifiable by being clearly attributed to reliable sources. Please help by adding sources to the article you created and by making it clear how the sources support the material. See here for how to do inline referencing. Many thanks! PS If you need any help, you can look at Help:Contents/Editing Wikipedia or ask at Wikipedia:New contributors' help page, or just ask me. ErikHaugen (talk | contribs) 19:01, 4 December 2013 (UTC)[reply]

And thanks for adding some! ErikHaugen (talk | contribs) 18:26, 30 December 2013 (UTC)[reply]

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Nanite, thanks for your article Thermal transpiration. Writing an article about a technical topic for a general audience is, needless to say, but one thing that helps is to include a section on practical applications. Is thermal transpiration an important part of any consumer products or manufacturing? I feel this would greatly help the article. Ego White Tray (talk) 04:40, 30 December 2013 (UTC)[reply]

Metal–semiconductor junction says "M–S junctions can either be rectifying or non-rectifying. The rectifying metal–semiconductor junction forms a Schottky barrier, making a device known as a Schottky diode, while the non-rectifying junction is called an ohmic contact." Non-rectifying junction redirects to ohmic contact, but that article doesn't define the term, after this edit you made. Can you update the ohmic contact article to define the term non-rectifying junction and contrast it with ohmic contact since I believe you mean that the terms are not equivalent. I take it that there is a difference between a metal–semiconductor ohmic contact and a generic ohmic contact. Or maybe nonrectifying junction should redirect to Metal–semiconductor junction if it only applies to those. I'm not a physicist, and physics was not my best subject in school, so I defer to you. Thanks, Wbm1058 (talk) 17:23, 16 January 2014 (UTC)[reply]

Ah, my bad. I didn't realize nonrectifying junction linked to there as well, and it's a good point to emphasize that the article is mainly about semiconductors. The lead should be better now, let me know what you think. Nanite (talk) 18:31, 16 January 2014 (UTC)[reply]

Thanks, that seems better. See also electrical junction, that might benefit from an expert's attention too. Wbm1058 (talk) 19:50, 16 January 2014 (UTC)[reply]

Hello Nanite, I see you have done some work on the Criticality Accident article. Could you please have a look at my proposal for a definition of Criticality? Thanks!--Graham Proud (talk) 04:09, 3 February 2014 (UTC)[reply]

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I thought I would go off the subject of our discussion of Gibbs paradox. I am an ex plasma physicist who left Solid State physics in my first year of graduate school because the theory seemed incomprehensible. For example, where was the proof that electrons accelerated according to their 'effective mass' when subjected to an electric field? (I now understand that the proof almost certainly exists somewhere, but an introductory book (e.g. Kittel) had no space to fill in every little detail).

You can do original research on Wikiversity. It is a very quiet and obscure place where you can tinker around with ideas for articles. Your thoughts on Gibbs paradox are in a somewhat obscure place in Wikversity (obscure²!) Someday, Wikipedia will have a good (or at least mediocre) article on every possible subject. Talented writers with offbeat ideas will have nowhere else to write than places like Wikiversity.--guyvan52 (talk) 02:36, 18 February 2014 (UTC)[reply]

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Hi Nanite,

I have a couple minor patches I would like to submit to your thermocouples_reference python module. Since I couldn't find a better way of getting in touch with you, they are pasted below. The first one allows the module to work under python 2.6. The second fixes an error in inverse_CmV when Tstart is not None.

Thanks, David Irving dhirving@gmail.com

--- thermocouples_reference_orig/function_types.py	2014-07-15 14:27:19.977844635 -0700
+++ thermocouples_reference/function_types.py	2014-07-15 14:53:20.934074420 -0700
@@ -69,7 +69,7 @@
         return self.table[-1][1]
     
     def __repr__(self):
-        return "<piecewise polynomial+gaussian, domain {} to {} in {}, output in {}; {} calibrated, from {}>".format(
+        return "<piecewise polynomial+gaussian, domain {0} to {1} in {2}, output in {3}; {4} calibrated, from {5}>".format(
             self.minT, self.maxT,
             Tunits_short[self.Tunits], Vunits_short[self.Vunits],
             self.calibration, self.source)
@@ -244,15 +244,15 @@
         Compute electromotive force for given thermocouple measurement junction
         temperature and given reference junctions temperature.
         
-        This method uses {} temperature units and {}.
+        This method uses {0} temperature units and {1}.
 
         Parameters
         ----------
         T : array_like
-            Temperature or array of temperatures (in {}).
+            Temperature or array of temperatures (in {2}).
         Tref : float, optional
-            Reference junctions' temperature (in {}),
-            defaults to {}.
+            Reference junctions' temperature (in {3}),
+            defaults to {4}.
             If derivative != 0, Tref is irrelevant.
         derivative : integer, optional
             Use this parameter to evaluate the functional derivative of
@@ -266,9 +266,9 @@
         Returns
         -------
         emf : array_like
-            computed emfs (in {})
+            computed emfs (in {5})
             or, if derivative != 0,
-            emf derivative (in {} / {}**derivative)
+            emf derivative (in {6} / {7}**derivative)
         """.format(Tlong, Vlong, Tshort, Tshort, Tref_default,
                    Vshort, Vshort, Tshort)
         return f
@@ -290,30 +290,30 @@
         You must have SciPy installed to use this method.
         (see documentation of .func.inverse for more notes on implementation)
         
-        This method uses {} temperature units and {}.
+        This method uses {0} temperature units and {1}.
         
         Parameters
         ----------
         emf : float
-            The measured voltage (in {}).
+            The measured voltage (in {2}).
         Tref : float, optional
-            The reference junctions' temperature (in {}).
+            The reference junctions' temperature (in {3}).
             This allows you to perform cold-junction compensation. Note that
-            Tref = {}, the default, corresponds to the reference junctions
+            Tref = {4}, the default, corresponds to the reference junctions
             being at the freezing point of water.
         Tstart : float, optional
-            Suggested starting temperature (in {}).
+            Suggested starting temperature (in {5}).
             You can hasten the search convergence by providing a good starting
             guess here. If not provided, the midpoint of the entire temperature
             range will be used.
         Vtol : float, optional
-            Tolerance of voltage in search (in {}),
-            defaults to {}.
+            Tolerance of voltage in search (in {6}),
+            defaults to {7}.
         
         Returns
         -------
         T : float
-            Junction temperature (in {}), such that:
+            Junction temperature (in {8}), such that:
               emf == func(T) - func(Tref)    (to within Vtol)
         """.format(Tlong, Vlong, Vshort, Tshort, Tref_default, Tshort,
                    Vshort, Vtol_default, Tshort)
@@ -390,8 +390,8 @@
         self.composition = composition
     
     def __repr__(self):
-        rng = "{:.1f} to {:.1f}".format(self.func.minT,self.func.maxT)
-        return "<{} thermocouple reference ({} {})>".format(
+        rng = "{0:.1f} to {1:.1f}".format(self.func.minT,self.func.maxT)
+        return "<{0} thermocouple reference ({1} {2})>".format(
                 self.type, rng, Tunits_short[self.func.Tunits])
     
     @property
@@ -496,4 +496,4 @@
         T = T*imul + iadd
         return T
 
-#end of module
\ No newline at end of file
+#end of module



--- a/thermocouples_reference/function_types.py
+++ b/thermocouples_reference/function_types.py
@@ -453,7 +453,7 @@ class Thermocouple_Reference(object):
         #mul, add = self._mats_Tunits_from['C'][0]
         #Tref = Tref*mul + add
         f_ref = self.func(Tref)
-        if Tstart != None: Tstart = Tstart*mul + add
+        #if Tstart != None: Tstart = Tstart*mul + add
         T = self.func.inverse(emf+f_ref,
                     Tstart=Tstart, Vtol=Vtol)
         #imul, iadd = self._mats_Tunits_to['C'][0]