 Clausius inequality (source code)

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= Clausius inequality
{c}
{title2=$\oint\delta Q/T\leq0$}

For a thermodynamic cycle, with heat positive into the system and each transfer divided by the absolute <temperature> of the relevant thermal boundary or reservoir, the cyclic integral is nonpositive. Equality holds for a reversible cycle. Closing an arbitrary process by a reversible return path yields $\Delta S\geq\int\delta Q/T$, because the reversible integral defines the <entropy> difference. The difference is the nonnegative <entropy production>; <entropy> transferred with heat need not itself be positive.

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