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arXiv · 2608.30421

d'Q = TdS for Infinitesimal Irreversible Processes: On the Differential Form of the Clausius Inequality

Hiroshi Shimahara
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Abstract

Conventionally, the differential form of the Clausius inequality is adopted for infinitesimal irreversible processes. We show that the correct first-order form for infinitesimal quasi-static irreversible processes is the equality d'Q=TdS rather than d'Q < TdS. This provides a purely thermodynamic proof that internal entropy production is second-order or higher and confirms that entropy remains a well-defined state quantity even when quasi-static irreversible processes are included, without resorting to the Boltzmann relation.

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Hiroshi Shimahara. 2026-08-31. d'Q = TdS for Infinitesimal Irreversible Processes: On the Differential Form of the Clausius Inequality. https://arxiv.org/abs/2608.30421

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