An Extended Second Law of Thermodynamics

TL;DR

This work addresses whether the standard second law of thermodynamics remains valid for systems with negative absolute temperature (NAT). It introduces an extended second law (ESL) defined by sign(T) dS >= 0, which reduces to the conventional law for $T>0$ but remains applicable when $T<0$. The authors illustrate the ESL with two representative NAT systems: Loop Quantum Cosmology near the quantum bounce and Onsager's vortices in bounded 2D fluids, showing that the ESL extends the domain of thermodynamic validity beyond the SSL. They discuss a phase-transition interpretation of the temperature sign change and highlight the role of bounded phase space and isolation in enabling NAT. The work provides a framework to reconcile NAT with thermodynamics and suggests broader tests in other NAT-bearing 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.