d'Q = TdS for Infinitesimal Irreversible Processes: On the Differential Form of the Clausius Inequality
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Shimahara, Hiroshi
Institution: Hiroshima University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204892134