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1) Entropy is supposed to be a state function so shouldn't any loop on the PV plane bring the system to its initial state and thus its initial entropy? Pair of values $P,V$ may not be enough to specify the state of the system, there may be other thermodynamics state variables. If so, it is possible system returns to the same values $P,V$, but it is in a ...

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But when I take it through an adiabatic reversible process to the same state as I did in the irreversible process, You assume this is possible, but nobody has succeeded doing so. If someone did, it would contradict the second law of thermodynamics for the reason you mentioned.

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If the process was reversible via the exact route taken to provide the current state then the creation of the initial state becomes indeterministic by definition. This violates the conservation of information, reversibility occurs via a different path, with one path entering and exiting each state of the system in its phase space.

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Reversible by definition means to back to the original state through exactly reversing your path. So by definition you must go through each and every step. It is clear why you can't retrace your steps one by one, because there are non! intermediate "states" are not states of equilibrium, because rapid change (faster than the speed of information in the ...

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