TY - JOUR
T1 - Origin of negative temperatures in systems interacting with external fields
AU - Calabrese, Salvatore
AU - Porporato, Amilcare Michele M.
N1 - Funding Information:
We gratefully acknowledge the comments of two anonymous reviewers. This work was supported through the US National Science Foundation (NSF) grants EAR-1331846 and FESD-1338694 and through the Carbon Mitigation Initiative at Princeton University .
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/6/26
Y1 - 2019/6/26
N2 - 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.
AB - 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.
KW - External field
KW - Gravitational field
KW - Ideal gas
KW - Magnetic field
KW - Negative temperatures
KW - Paramagnetic system
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U2 - 10.1016/j.physleta.2019.04.027
DO - 10.1016/j.physleta.2019.04.027
M3 - Article
AN - SCOPUS:85064694855
SN - 0375-9601
VL - 383
SP - 2153
EP - 2158
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 18
ER -