Why don't we have heat circuits? Common circuits use electricity to transmit power and signals.
I know we transfer heat power using things like HVAC (heating, ventilation, and air conditioning).
I don't know anything that encodes/modulates information and transmits it via heat. There are systems with heat as a feedback signal, but they aren't modulating some completely independent information (say the stock market prices) onto the heat signal. I imagine entropy makes it harder to use heat as information, but there should still be some ways to? Even if not industrial there should be some scientific paper about it.
So I don't know of any existing heat circuits, in industry or in academia. Why is that? Ex: a calculator which does calculations via the processing of heat signals (not an electrical calculator that is merely powered by heat).
 A: Here are a few reasons:

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*As noted by Slereah in the comments, signals would propagate much slower: by roughly a factor of $10^5$.


*Thermal conductivities of common materials vary by about a factor of $10^5$ between the most thermally conductive and insulating objects. For electrical conductivities it is $>10^{20}$. This means that you can have nearly perfect electrical conductors and insulators, while for a thermal signal the problems of stray resistances and leakage would be much more severe. There are at least two fundamental reasons for this: heat can be transmitted by more channels than current, and current can fundamentally depend on quantum tunneling of electrons while heat does not require any physical object to be transported.


*While it appears that thermal inductors can be created, they are not nearly as convenient as electrical inductors (the linked article demonstrates a mechanism involving a Peltier cooler, which means that it is an active device in contrast to a passive electrical inductor). Similarly, it seems that thermal diodes have been demonstrated but they are an active area of research, and thus presumably not nearly as easy to realize as electrical ones.
