A Surprising Thing About Thermodynamics and Reservoirs

It is quite fashionable to state that one cannot take energy from a reservoir at constant temperature. Well, that is not quite true as stated.  More rigorously, we cannot take energy from a reservoir in equilibrium at constant temperature.  We can indeed take energy from a reservoir at constant temperature but not in equilibrium.  That is, from a nonhomogeneous reservoir at constant temperature.

We quote Hsu-Chieh Yeh { [40] } for a vivid statement of this fact:

From Planck’s statement of the second law of thermodynamics it is generally inferred that it is impossible to construct an engine which produces work at the expense only of heat taken from the air or the ocean.  …[It is demonstrated that]… when the air and the ocean are combined as a nonhomogeneous reservoir of uniform temperature, it is possible to construct an engine which produces work by extracting heat from the said reservoir.  This does not constitute a violation of the second law of thermodynamics, rather that the “reservoir” in the Planck’s statement must be clearly stated as being in equilibrium."

The proof and a schematic diagram of a machine to successfully do that energy extraction process is shown by Yeh { [41] }.

The "Final Word" On the Conservation of Energy Law

            Some arch skeptics are fanatically die-hard—and a real pain in the neck as well. 

To be absolutely precise, they have no leg to stand on, if they accept what physics ultimately says on the subject of energy conservation.

Before one gets too adamant about the universality of energy conservation, here's a most astonishing thing, but quite true:  In general relativity there is at basis no such thing as conservation of energy at all, unless one first makes some assumptions to inject it artificially so as to avoid facing the sheer terror of the collapse of energy conservation!

The great Hilbert pointed this out shortly after the advent of Einstein's theory of general relativity.  E.g., quoting from Logunov and Loskutov { [42] },  p. 179:

"In formulating the equivalence principle, Einstein actually abandoned the idea of the gravitational field as a Faraday-Maxwell field, and this is reflected in the pseudotensorial characterization of the gravitational field that he introduced.  Hilbert was the first to draw attention to the consequences of this.  In Ref. 2 [D. Hilbert, Gottingen Nachrichten, Vol. 4, 1917, p. 21] he wrote:  'I assert... that for the general theory of relativity, i.e., in the case of general invariance of the Hamiltonian function, energy equations... corresponding to the energy equations in orthogonally invariant theories do not exist at all.  I could even take this circumstance as the characteristic feature of the general theory of relativity.'  Unfortunately, this remark of Hilbert was evidently not understood by his contemporaries, since neither Einstein himself nor other physicists recognized the fact that in general relativity conservation laws for energy, momentum, and angular momentum are in principle impossible."

For situations where serious general relativity is not terribly involved, then we can legitimately speak of conservation of energy.  Even so, one should not be too hasty to leap forth with the old equilibrium thermodynamics and pontificate that "there's no such thing as an overunity EM system because that would violate the  infamous second law".  If it's an open system far from equilibrium, classical thermodynamics and that second law do not even apply.  The skeptic then objecting on the grounds of equilibrium thermodynamics is revealing that he doesn't know the difference between systems in equilibrium and open systems not in equilibrium.  In short, he simply does not understand thermodynamics, and it is useless to argue with such a critic.

Before one gets overly confident about ordinary electrical and electronic circuits, and concludes that it's the rarest thing in all the world to have out-of-equilibrium operation in them, one should read the literature carefully.  To the contrary, in all sorts of circuits, equilibrium often is unexpectedly departed from, leading to chaotic operation and a highly increased degree of system complexity.  E.g., quoting fromOgorzalek { [43] }, p. vii:

“All real systems are nonlinear in nature.  This simple observation is true also for electrical and electronic circuits even though many of them are designed to perform linear transformations on signals.  …in many cases the designed circuit, when implemented, performs in a very unexpected way, totally different from that for which it was designed.  In most cases, engineers do not care about the origins and mechanisms of the malfunction; for them a circuit which does not perform as desired is of no use and has to rejected or redesigned….”

“…electrical and electronic circuits constitute a group of real physical systems in which observations and measurements are relatively easy to make. ..Such an ‘experimental comfort’ enabled thorough studies confirming the existence of strange unexpected behavior in almost every type of electronic circuit – oscillators, filters, instrumentation circuits, power supplies, PLLs, electric machines, microwave circuits, electro-optic systems, etc.  The main problem remains in interpreting experimental data.”

In other words, normal circuits indeed do often depart from expected equilibrium behavior.  Engineers just shrug and "fix the circuit where it doesn't do that".  The scientists are aware of such occurrences, but have not yet fully deciphered all the ramifications or the wild phenomena that result.  But they are working on it!