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In particular, William Thomson (Kelvin) appeared to be wrong about key things in physics (initially X-rays, aether, even aviation feasibility).,_1st_Baron_Kelvin#Pronouncements_later_proven_to_be_false

Are there any theories that contradict the idea that a heat differential must exist in order to convert heat energy to another form (causative) vs a heat differential being a secondary effect? I have seen some discussion about the potential for room-temperature thermionics (and whether or not that by definition relies on a heat differential to function?)

If such a device existed to convert heat without a 'classical' heat differential being a primary causative of the conversion, what implications would it have for irreversibility?

How does a purely homogeneous heat / kinetic energy pool in the classical sense behave when considering different atoms / elements with the same kinetic energy at the atomic level? Is it possible that different elements can never truly have the same kinetic energy in such a case, causing a situation where an exploitation can be found to do the conversion of energy? One hypothesis could be that heterogeneous atomic mixtures is the true cause of brownian motion (unless this has been proven to not be the case). In other words, is it not the case that homogeneous bulk matters behave predictably at any given kinetic energy level (heat)? This would have implications for the brownian ratchet being based on randomness, when in fact physical matter could potentially be biased to a predictable movement (even if only in a very confined system, i.e. nano-scale), where possibly extremely small kinetic differences can be engineered and exploited to generate electricity (or mechanical movement useful for work) from a single reservoir of heat, disproving the Kelvin statement.

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The first sentence, as an "introduction to Lord Kelvin" (and therefore probably the motivation behind this question as well), is a totally dishonest piece of propaganda, a libel that Kelvin's relatives should sue you for and financially destroy you. Lord Kelvin was the #1 guy who really unified modern physics into the form that could lead to physics departments, a culiminating character of classical physics, one of the top five figures behind thermodynamics, especially its laws. He surely doesn't deserve to be trashtalked by nobodies. Selective search for Lord Kelvin's errors is dishonest, too – LuboŇ° Motl Aug 5 '12 at 4:39
Otherwise heat differential is obviously needed to convert heat to useful energy, that's what the second law of thermodynamics is all about - a law that Lord Kelvin formulated particularly cleanly. If there's no heat differential, you mean temperature gradient, then one is at thermal equilibrium and no mechanical work or otherwise useful work may be extracted from it. So better get back to school and learn pillars of classical physics, so much contributed to by Lord Kelvin, before you jump to the Internet and start to spread completely unjustifiable insults of giants. – LuboŇ° Motl Aug 5 '12 at 4:45
So you are saying you cannot entertain any theories against 'Lord Kelvin' and his 'Kelvin Statement' of the second law of thermodynamics? Doesn't this paper: indicate a theory against Thomson's 'statement'? If you can entertain ideas and findings from those very likely more qualified, please do, otherwise don't be so long-winded in saying you can't :/ Saying I should be financially destroyed for pointing out Thomson's silly thoughts, is complete nonsense. – CatBauer24 Aug 6 '12 at 5:01

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