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d'Q = TdS for Infinitesimal Irreversible Processes: On the Differential Form of the Clausius Inequality
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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BibTeX
@misc{shimahara2026infinitesimal,
title = {{d'Q = TdS for Infinitesimal Irreversible Processes: On the Differential Form of the Clausius Inequality}},
author = {Hiroshi Shimahara},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30421},
eprint = {2608.30421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30421},
}
RIS
TY - UNPB
TI - d'Q = TdS for Infinitesimal Irreversible Processes: On the Differential Form of the Clausius Inequality
AU - Hiroshi Shimahara
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30421
UR - https://arxiv.org/abs/2608.30421
AB - 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.
ER -