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.

First of them is mechanical way, when a vessels with a salt and fresh water are separated by a semi-permeable membrane. The disadvantage of this way is high energy loss during electricity generation, because electric power generates in two stages.
The second one uses ion selective membranes. In this case electric power generates in one stage. The disadvantage of second way is a high resistance of ion-selective membranes.
We develop the third way of converting entropy of fresh and salt water mixing into electrical energy, using concentration galvanic cell.

Of course NaCl solution is not the best working solution for concentration galvanic cell. We may use Ag/AgCl electrode, but they are too expensive for high-scale generation.
So we have such a scheme of our cell:

salt water || semi-permeable membrane || working solution of high concentration|| porous diaphragm ||working solution of low concentration || semi-permeable membrane  || fresh water.

Figure 1. Concentration galvanic cell

In the picture: C₂>C₁

The osmotic pressure at the working solution of low concentration is higher, then osmotic pressure at fresh water, so the water passes through the semi-permeable membrane into concentration galvanic cell and maintains a low concentration of the electrolyte near the first electrode.

The osmotic pressure at the salt water is higher, then osmotic pressure at working solution of high concentration, so the water passes through the semi-permeable membrane out from concentration galvanic cell and it maintains a high concentration of the electrolyte near the second electrode.

So, NaCl solution never takes part at the reaction, but absorbs water from working solution of high concentration!

Elements from Figure 1 could be connected in a cascade:

Figure 2. Cascade of cells.

Also interesting results could be obtained by using sulfuric acid as working solution and Pb/PbSO₄ electrodes.

In contrast to the traditional concentration galvanic cells, where the potential difference depends of the  lg c₁/c₂, in sulfuric acid solution we have practical linear dependence of the electrode potential on the concentration of sulfuric acid. We have this effect because galvanic cell uses not only entropy factor, but also the energy of exothermic reaction of sulfuric acid dissolving in the water.