Origin of Negative Temperatures in Systems Interacting with External Fields

TL;DR

This paper clarifies that negative temperatures in systems with external fields result from misattributing interaction energy as internal, and proposes a proper thermodynamic approach to avoid such misconceptions, with implications for thermodynamic laws.

Contribution

It demonstrates how negative temperatures arise from energy misattribution in external field interactions and offers a corrected thermodynamic formalism to prevent this misconception.

Findings

Negative temperatures stem from incorrect energy attribution.

Proper formalism avoids negative temperatures in external field systems.

Super-Carnot efficiencies are inconsistent with correct thermodynamics.

Abstract

The controversial existence of negative temperatures has stirred interesting debates that have reached the foundations of thermodynamics, including questions on the second law, the Carnot efficiency and the statistical definition of entropy. Here we show that for systems interacting with an external field, negative temperatures arise from an energy mis-attribution in which the interaction energy with the field is treated as a form of internal energy. We discuss how negative temperatures are avoided when using a proper thermodynamic formalism, which accounts for the intensive and extensive variables associated to the external field. We use the paramagnetic system and a perfect gas in a gravitational field to illustrate these ideas. Considerations about the isothermal and adiabatic work done by the field or the system also shed light on the inconsistency of super-Carnot efficiencies.