The thermodynamics of the thermocouple is rather simple: the electrical power, produced by the thermocouple:

P_e=a * (T₁-T₂ )* I,

where a is the Seebeck coefficient ,

T₁-T₂ is the temperature difference,

I is a current .

As a result of this current, which flow through the contact, Peltier heat is released or absorbed. The power of Peltier heat releasing or absorption:

P_h=a * T * I, where T is the absolute temperature.

The Efficiency of ideal thermocouple without heat transfer from hot to cold exposure would be equal to the ratio of electrical power to thermal power:

η=P_e/P_h=(T₁-T₂ )/T₁
As we can see , the efficiency of an ideal thermocouple does not depend on the Seebeck coefficient and is equal to the efficiency of Carnot cycle .
In real thermocouples heat transfers from the hot to the cold contact. It is necessary to decrease this useless heat transfer to increase the efficiency of thermocouple. The problem is that good conductors of electricity and are good conductors of heat. A good heat insulators are also good electricity insulators. DC current through them will not work.

Concept of AC thermocouple.
Quite another matter -AC . The two conductors separated by a dielectric is a capacitor. Capacitor for AC is not a barrier.
Thermocouple AC , in which the hot and cold junction are separated by a thermo insulating dielectric ( or vacuum) would be closer to the ideal thermocouple , and its efficiency would be closer to efficiency Carnot cycle .
The question arises as to change the sign to get the thermocouple emf not swapping hot and cold junction ?

We have an idea to use longitudinal Nernst – Ettingshausen effect.

Seebeck coefficients of metals or semiconductors are changed in a magnetic field. According literature data in magnetic field B=1 Tesla Seebeck coefficients could be 400-500 microvolts per kelvin[1].
Schematic diagram of the AC thermocouple is shown in Fig. 1.

Fig. 1. The Scheme AC thermocouple with external source of magnetic field

Thus, the entire thermal element consists of the one and the same material. The magnetic field is alternately switched on in the area of the capacitor 1 , the area of ​​the capacitor 2. The thermoelectric power will change sign. According to the literature date, bismuth is the material with the highest values of longitudinal Nernst – Ettingshausen effect.

It is possible to use own magnetic field of the current for Seebeck coefficient changing. The scheme of thermocouple with internal source of magnetic field is presented at Fig.2.

Fig. 2. The Scheme AC thermocouple with internal source of magnetic field

Depending on the direction of the current, magnetic field generated in the capacitor area of the capacitor 1 or 2. Of course, electromotive force of a single thermocouple is too small to ensure proper operation of the diodes, so the device consists of many thermocouples connected in series, two diodes and two coils.

 Conclusions.

1. The efficiency of thermocouples is low because of high thermal conductivity of thermocouple materials.

2. This problem is very hard to solve in DC thermocouples, because good electricity conductors are good heat conductors too.

3. It is more easy to keep temperature gradient in AC circuit, consist of conductors and capacitors, because dielectric or vacuum of a capacitor will be a a thermo insulator.

4. A concept of alternating current thermocouple, based on longitudinal Nernst – Ettingshausen effect, was developed.