What is nonlocal resistance?

Question

We are first taught to calculate local resistance, where current and voltage are on the same part of the material.

But many experiments measure nonlocal resistance, where current and voltage are measured on different parts of the material.

1. What is nonlocal resistance?

2. What is the advantage of measuring nonlocal resistance than its local counterpart?

3. How to calculate nonlocal resistance?

4. If local resistance increase, is it a must that nonlocal resistance must increase too?

Answer 1

1. Nonlocal resistance is the ratio of the current in a material to the voltage between some other two points. It is a much less useful quantity, because this depends on the details of induced changes on the conductor and elsewhere to determine, it isn't something that is determined only by local material quantities.

2. The only advantage is that you can measure it away from the material, if you can't stick a probe in. It can be measured using the electric field far away from the material. The disadvantage is that you then have to break your head to figure out what is going on inside the conducting material itself, which is what you usually care about.

3. The ratio of voltage to current, where voltage is between to other points.

4. In the linear regime, with only materials with linear response and conductors around, the answer is always yes, with one important caveat--- if the resistance is negative (meaning you measured the voltage between two points which for some reason have the opposite voltage than two points at successive position in the wire), it gets more negative as you increase the current, so it technically goes down. The precise statement is that if you multiply the current by a factor of k, you also multiply the additional voltage elsewhere by a factor of k, so it's a linear relationship.