Thomson's formulation of the second law: an exact theorem and limits of its validity

TL;DR

The paper proves Thomson's formulation of the second law for macroscopic systems, explores its limitations for mesoscopic sources, and discusses the Clausius principle, highlighting conditions where work extraction and heat flow principles may not hold.

Contribution

It provides an exact proof of Thomson's formulation for macroscopic sources and identifies its limitations in mesoscopic regimes, supported by solvable models.

Findings

Thomson's law holds for macroscopic sources of work.

Work extraction from a thermal bath is possible at high temperatures in mesoscopic systems.

The Clausius principle has specific conditions for its validity.

Abstract

Thomson's formulation of the second law - no work can be extracted from a system coupled to a bath through a cyclic process - is believed to be a fundamental principle of nature. For the equilibrium situation a simple proof is presented, valid for macroscopic sources of work. Thomson's formulation gets limited when the source of work is mesoscopic, i.e. when its number of degrees of freedom is large but finite. Here work-extraction from a single equilibrium thermal bath is possible when its temperature is large enough. This result is illustrated by means of exactly solvable models. Finally we consider the Clausius principle: heat goes from high to low temperature. A theorem and some simple consequences for this statement are pointed out.