Clausius–Duhem inequality

The Clausius-Duhem inequality is a fundamental principle in thermodynamics and continuum mechanics that expresses the second law of thermodynamics in a differential form. It serves as a mathematical statement of the irreversibility of thermodynamic processes and the concept of entropy production. In simple terms, the inequality can be stated as follows: \[ \frac{dS}{dt} \geq 0 \] where \( S \) is the entropy of a system.