Origin of negative temperatures in systems interacting with external fields

Salvatore Calabrese, Amilcare Michele M. Porporato

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 may arise when the interaction energy with the field is treated as a form of internal energy. We discuss how negative temperatures are avoided when using a thermodynamic formalism that 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.

Original languageEnglish (US)
Pages (from-to)2153-2158
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number18
StatePublished - Jun 26 2019

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • External field
  • Gravitational field
  • Ideal gas
  • Magnetic field
  • Negative temperatures
  • Paramagnetic system


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