![]() ![]() The picture is of an outward-progressing spiral, an unrolling from an infinitesimal beginning through ever broadening circles, until finally all reality is embraced within. The word "evolution" is of course derived from a Latin word meaning "out-rolling". The very terms themselves express contradictory concepts. If the entropy principle is really a universal law, then evolution must be impossible. Evolution and entropy are opposing and mutually exclusive concepts. The law of increasing entropy is an impenetrable barrier which no evolutionary mechanism yet suggested has ever been able to overcome. Not only is there no evidence that evolution ever has taken place, but there is also firm evidence that evolution never could take place. ![]() There is one consideration, however, which goes well beyond the implications of the above difficulties. Similarly the great gaps in the fossil record make it extremely doubtful that any genuine evolution, as distinct from small changes within the kinds, ever took place in the past. The sequence of cycles is repeated using heat reservoirs at appropriate temperatures, until the two bodies arrive at a common temperature T f.The study of biological processes and phenomena indicates that significant evolutionary developments are not observable in the modern world. Furthermore, the temperature of the hot body is reduced to T 1 − δ T 1 and that of cold body rises to T 2 + δ T 2, thus decreasing the difference between their temperatures. As a consequence, the sum of the entropy changes in the bodies is also zero. In this whole process, the engine and the auxilliary reservoirs undergo a reversible process, so their total change in entropy is zero. This heat is then reversibly transferred to the cold body at T 2. Now, an infinitesimal amount of heat dQ 1 is reversibly transferred from the hot body to the reservoir at T 1 − δ T 1, a reversible heat cycle is run, which outputs work dW and rejects heat d Q 2 = d Q 1 − d W to the reservoir at T 2 + δ T 2. Now, assume that we have another pair of reservoirs, which differ from the initial pair by infinitesimally different temperatures, denoted as T 1 − δ T 1 and T 2 + δ T 2, where δ T i > 0. To visualize one such infinitesimal heat cycle-say, the first one-we have prepared the two bodies in initial states using reservoirs at temperatures T 1 and T 2. The envisaged reversible step requires the presence of a heat engine, a reversible work source, and a set of auxiliary heat reservoirs. We argue below that T F > T f holds not only for the case with algebraic means but also in general. Therefore, we can say that the condition T F > T f directly implies Δ S > 0. (3) may be reexpressed as Δ S = ( C 1 + C 2 ) ln ( T F / T f ). 14 Now, T f is determined by the reversibility condition: C 1 ln ( T f / T 1 ) + C 2 ln ( T f / T 2 ) = 0, yielding T f = T 1 α T 2 1 − α. 1,12,13 This may be achieved by introducing a heat engine and running infinitesimal, reversible heat cycles that gradually reduce the temperature difference between the two bodies, until the two bodies obtain a common temperature T f. More precisely, consider a reversible process that extracts work from the two bodies initially at temperatures T 1 and T 2. 2–11 However, the fact that one of the means in the above comparison, T 1 α T 2 1 − α, is also the final common temperature of the two bodies when subjected to the process of reversible work extraction, seems to have escaped attention in the literature so far. There has been previous discussion around this apparent correspondence between physical laws and mathematical facts such as these inequalities. In this case, the proof of the inequality Δ S > 0 rests on the inequality between weighted arithmetic and geometric means, given by α T 1 + ( 1 − α ) T 2 > T 1 α T 2 1 − α, for T 1 ≠ T 2. ![]()
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