fluidistic
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I honestly do not know the reason(s). Of course not.Philip Koeck said:Is that because those effects would lead to perpetual motion machines?
Here is what I can think on the top of my head:
I would guess that early scientists (Thomson, Bridgman, Altenkirch, Callen, Domenicali and Ioffe amongst others) considered cases that made sense with the kinds of materials available at their times. They did not consider more general cases, or "exotic" cases that we have nowadays. And scientists from nowadays are still missing, due to inertia (and possibly the lack of good up to date textbook on thermoelectricity), what they can achieve with thermoelectricity. Some of them (e.g. Uchida https://aip.scitation.org/doi/full/10.1063/5.0077497, and Snyder's https://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.045202) are hinting at nice novelties, but they are still missing a lot (that I can think of).
Also, what you may be missing is that maybe you shouldn't focus on heat (or heat flux/transfer) only when you deal with the thermoelectric case, but maybe you should look at the energy flux ##\vec J_U = \vec J_Q+\overline{\mu}/e\vec J_e##. Energy as in the "internal energy U" of thermodynamics. I'll repeat myself hopefully a last time, there's a very quick way to see that heat can flow from cold to hot just by looking at the generalized Fourier's law that appear in most thermoelectric books (and Wikipedia), ##\vec J_Q =-\kappa \nabla T + ST \vec J_e##. Where ##S##, the Seebeck coefficient can have either sign, ##\vec J_e## can have any direction since it's the current density and you can engineer the current to go in any direction you want and also any reasonable magnitude. It is clear that you can make a system where ##ST \vec J_e## outweights ##-\kappa \nabla T##. When this happens, heat flows from cold to hot (or in another direction if you want it to be so and arrange it that way). If you are unable to convince yourself by looking at this simple relationship, there's nothing else I can do to convince you. This doesn't break thermodynamics laws. There's still an increase in entropy over time, and no energy is created out of thin air.