Logic and thermodynamics: the heat-engine axiomatics of the second law

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We challenge the statement that the principle of Thomson and the principle of Clausius are equivalent. A logical mistake in the supposed textbook proof of their equivalency is indicated. On this account we refine the heat-engine axiomatics. We consider the energy exchange in the configuration comprised of two heat reservoirs and one mechanical device and show explicitly the domains banned by the laws of thermodynamics.
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