An Extended Second Law of Thermodynamics

TL;DR

This paper extends the second law of thermodynamics to include negative absolute temperatures, broadening its applicability to new physical systems like quantum cosmology and vortices.

Contribution

It formulates an extended version of the first and second laws that applies to negative temperatures, expanding the fundamental principles of thermodynamics.

Findings

Extended laws recover conventional thermodynamics for positive temperatures.

Application to quantum cosmology and vortices demonstrates broader applicability.

Provides a theoretical framework for negative temperature systems.

Abstract

The second law of thermodynamics constitutes a fundamental principle of physics, precluding the existence of perpetual motion machines and providing a natural definition of the arrow of time. Its scope extends across virtually all areas of physical theory. Nonetheless, certain systems are known to admit negative absolute temperatures under well-defined conditions, a phenomenon that has been experimentally observed. In this work, we formulate an \textit{extended} version of the first and second laws, which recovers the conventional statement for positive temperatures and extends its applicability to the negative-temperature domain. Illustrative examples are discussed in the contexts of quantum cosmology and Onsager's vortices.