Origin of negative temperatures in systems interacting with external fields Academic Article uri icon


  • 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.

published proceedings


altmetric score

  • 0.5

author list (cited authors)

  • Calabrese, S., & Porporato, A.

citation count

  • 4

complete list of authors

  • Calabrese, Salvatore||Porporato, Amilcare

publication date

  • June 2019