If I'm thinking about this correctly, the voltage difference in a conductor between two points of unequal temperature occurs because the chemical potential is lower on the hotter side which causes electrons to bunch up there. Is this correct?

So at equilibrium, the macroscopic observation is such that the combination of chemical and electric potentials are constant throughout the wire (thus when the the chemical potential is lower, the electric potential is higher to compensate).

But my question is, how is it then "possible" to measure a voltage with a multimeter? Don't multimeters let a very small amount of current through in order to measure the voltage? But if the wire is in equilibrium, electrons would NOT move even if there is excess charge at one end. So how does this all work?

The short answer is that current does flow in that circuit.

In fact, the current makes the hot side cool down and the cold side warm up (this is known as the Peltier effect), so one must have a constant heat source. Think about it this way: if you were using a thermocouple to measure the temperature of a very small, heated sample inside some sort of insulator, you would want to connect the thermocouple to the voltmeter extremely briefly, so as to minimally disturb the temperature of the sample.

My question was, how is thermocouple voltage measured? What type of instrument can measure electric potential without requiring even a small current?

The type you buy at walmart won't work according to my understanding (which is right or wrong?) so then how are measurements done?

P.S. Forget about the thermal equilibrium... electrons reach their equilibrium millions of times faster than the heat, so don't bring up irrelevant things to make this more complicated.

You only read half of the explanation of the thermocouple. You cannot measure Seebeck voltages directly. You should read up on why thermocouples are made of dissimilar materials. If you use two materials with different Seebeck coefficients, that are connected on say the hot side and use a voltmeter between the two on the cold side there will be a current. One explanation would be like this:
If you apply a voltage to a material that is different than the equilibrium voltage, then current will flow. If you have two different materials the voltage difference between the ends is different. So if you connect them together current will flow in a circle, because one thermocouple leg is the voltage source for the other one.
If you use only one pure material it is impossible to measure a Seebeck voltage due to the reason that you have described.

You still don't get my question...

Just because there is a difference of ELECTRIC potential, it does not mean that the electrons will move from high electric potential to lower. This is only true in general if other potentials (i.e. the chemical potential which is important here) are constant.

A wire represents an equipotential medium... it means that no matter what material you are using, as long as it is conductive, will let electrons reach equilibrium (which takes something like a few nanoseconds or picoseconds).

Forget the Seebeck BS you learned, I'm talking about the Fermi gas theory from quantum statistical mechanics. Maybe I posted in the wrong section.

What type of instrument can measure electric potential without requiring even a small current?

None. Just like any other measuring device, it must interact with what's being measured in order to report anything. Technically speaking you cannot measure any electrical characteristic with zero interaction between the measurement device and the sample being measured.

Fundamentally speaking, it takes some energy to convey information. This is true of all systems. And somehow, the 'sample' needs to convey the voltage information to the measurement device. If not a single charge ever entered or exited the voltmeter while making the measurement, how would the voltmeter be able to 'know' anything at all?

If you are asking a more practical question, this link has good info: http://zone.ni.com/devzone/cda/tut/p/id/4237#toc2 [Broken]

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You can tell there is an electric potential by observing the electric field. But just because there is a field, it does not mean that (macroscopically) charge will move since the chemical potential is "holding it back".

I honestly don't see why this is hard to understand. If nobody knows, then don't worry about it....

My question was, how is thermocouple voltage measured? What type of instrument can measure electric potential without requiring even a small current?

The type you buy at walmart won't work according to my understanding (which is right or wrong?) so then how are measurements done?

P.S. Forget about the thermal equilibrium... electrons reach their equilibrium millions of times faster than the heat, so don't bring up irrelevant things to make this more complicated.

You read a thermocouple with a normal voltmeter which is able to measure very small voltages (ranges of tens of mV). For the rest, it's a normal voltmeter.
Some smart and expensive voltmeter, such as the one I have on my desk now, automatically convert the voltage to °K.

Normally, a voltmeter has a very high impedance, so that e.g. my tester is sinking a current of nano Amps. Virtually zero.

How much voltage or current can be obtained from a thermocouple, if heat equivalent to that expended by a fridge is passed through it?

Go buy a 10$thermocouple from home depot. Go buy a multimeter 5$ from non-franchise hardware store that will do mV.
Boil some water and dip the long end into it, read voltage.
You should be able to see what happens. Just do it.

I'm not really quite sure what you mean by chemical potential, but the thermoelectric effect happens because of a combination of 3 things:

1. Higher work-functions mean more stability. Electrons go to the metal with higher work-function. Electric field is generated, resists more from moving in
Overcome by:
2. Diffusion current given difference in e- density. Movement is from high concentration to low, analogous to many other things in nature.
3. Thermal expansion also affects work-function.

You still don't get my question...

Just because there is a difference of ELECTRIC potential, it does not mean that the electrons will move from high electric potential to lower. This is only true in general if other potentials (i.e. the chemical potential which is important here) are constant.

A wire represents an equipotential medium... it means that no matter what material you are using, as long as it is conductive, will let electrons reach equilibrium (which takes something like a few nanoseconds or picoseconds).

Forget the Seebeck BS you learned, I'm talking about the Fermi gas theory from quantum statistical mechanics. Maybe I posted in the wrong section.

Well the Seebeck ******** works really well, especially when you use the matrix form. Why do you think that there is an equilibrium for the electrons? If the magnetic fields are negligible, the Electric potential is well defined. And as long as there is a thermal gradient the charge carriers are moved in this gradient.
The process stops when the electrical current due to the Seebeck voltage cancels the current due to diffusion. With two materials the diffusion currents are different, but the voltage between the two ends of both wires must be the same (The E-Field is conservative) so in at least one wire the currents cannot cancel.
I guess in your picture the reason for the currents is the difference in the electrons chemical potential between the two materials.

You know, this OP is 4 months old. But the OP was given the wrong answer. NO current is required to measure thermocouple voltage. But no one challenged the guy with the wrong answers with basis rooted in pop culture quantum mechanical mythology.