Is the Clausius inequality a consequence of the second law?

TL;DR

This paper critically examines the Clausius inequality's foundations, demonstrating it is not universally derived from the second law and exploring potential violations through thought experiments and experimental detection possibilities.

Contribution

It challenges the assumption that the Clausius inequality is a direct consequence of the second law, providing theoretical analysis and thought experiments to support this.

Findings

Clausius inequality is not always a logical consequence of the second law.

Thought experiments show possible violations of the Clausius inequality.

Potential for experimental detection of violations is discussed.

Abstract

We present an analysis of the foundations of the well known Clausius inequality. It is shown that, in general, the inequality is not a logical consequence of the Kelvin-Planck formulation of the second law of thermodynamics. Some thought experiments demonstrating the violation of the Clausius inequality are considered. The possibility of experimental detection of the violation is pointed out.