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This theorem provides a dynamic foundation for the two equivalent statements of Second Law of Thermodynamics, à la Kelvin's and Clausius'. We show that in the long-time limit the entropy production of the finite driven system precisely equals the potential energy decrease in the lifted system. 1.4, it is impossible to construct a device that, operating in a cycle, will produce no effect other than the transfer of heat from a cold body to a hot one. The corresponding lifted processes have detailed balance thus a natural potential function but no stationary probability. The second law of thermodynamics can also be expressed in terms of the Clausius and Kelvin-Planck statements: Clausius statement: As shown in Fig. Carnot’s engine is the highest possible heat engine using hot and cold reservoirs. Kelvin-Planck statement: No device is possible whose sole effect is to convert a given amount of heat completely into work.
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Carnot’s Theorem states that the efficiency of an engine working irreversibly is always less than a reversible engine operating between the same two reservoirs while the efficiency of two reversible engines is the same. A surjective map is rigorously established through the lift when the state space is either a discrete graph or a continuous n-dimensional torus T n. Clausius Statement for Second Law of Thermodynamics: It is impossible to construct a device that operates in a cycle and produces no effect other than the. The second law of thermodynamics is derived from three statements.
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We provide a stochastic mathematical representation for Clausius' and Kelvin-Planck's statements of the Second Law of Thermodynamics in terms of the entropy productions of a finite, compact driven Markov system and its lift. 5 quotes have been tagged as second-law-of-thermodynamics: Charles Percy Snow: ‘A good many times I have been present at gatherings of people who, by the.5 quotes have been tagged as second-law.