
Fig. 1:
Ludwig Boltzmann (1844  1906), Austrian scientist
© The Dibner Library Portrait Collection  Smithsonian Institution



Fig. 2:
American mathematical physicist Josiah Willard Gibbs (1839 – 1903)
© Zeitschrift für Physikalische Chemie, Band 18, von 1895

 
Temperature quantifies our perception of 'hot' and 'cold'. Temperature
is also fundamental for predicting the efficiencies of machines that
convert heat into usable work. For decades, physics students have
learned that temperature is always positive when measured on the
Kelvin scale. An important consequence of this assumption is that the
efficiency of a heat engine is always smaller than one, i.e. only a
fraction of the energy put in as heat, e.g. by burning fuel in the
engine of a car, can be harnessed to perform useful work, like
propelling a car.
However, there have been both theoretical and experimental claims over
the past 60 years that there are certain systems with a negative
absolute temperature. Even though these are very special systems 
nuclear spin systems or ultracold atom gases – this would have
profound conceptual and practical consequences. Such systems might not
only facilitate the construction of hyperefficient heat engines. They
might also serve as a laboratory model for the mysterious Dark Energy,
which was postulated by astrophysicists to explain the accelerated
expansion of the Universe. “We actually have no idea what Dark Energy
is on a very fundamental level,” says Stefan Hilbert from MPA. “So we
wanted to find out if these results would indeed shed light on Dark
Energy.” This, however, meant going back to the basics of thermodynamics.
Most textbooks advocate the formalism introduced by Ludwig Boltzmann
to relate the thermodynamic temperature of a system to its internal
structure. For many systems, this formalism works just fine. However,
"when we examined Boltzmann's definitions in detail, we found serious
inconsistencies that lead to nonsense results for many systems," says
Stefan Hilbert. Dunkel and Hilbert found that these inconsistencies
can be avoided by using a slightly different formalism that was
derived by Gibbs already more than 100 years ago, but has mostly
been forgotten since then.
A feature of Gibbs' formalism is that temperature never becomes
negative. As Dunkel and Hilbert show, the number determined in recent
experiments claiming negative temperatures in ultracold atom gases is
not the actual thermodynamic temperature, but rather a complex
function of temperature and another quantity, known as heat
capacity. The thermodynamic temperature in fact remained positive in
these experiments, which makes it less likely that these systems
behave like Dark Energy.
“In most cases, the difference between the Boltzmann temperature and
the Gibbs temperature is negligible,” explains Stefan Hilbert. “But in
extreme physical conditions, as is the case for these systems with
allegedly negative temperature, only Gibbs provides the correct
description.” To directly test this, Dunkel and Hilbert propose a
straightforward experiment: If there is a single atom in a trap that
allows the atom to move only in one direction, then the pressure
should be negative at both ends if the Boltzmann description is
correct, while the pressure should be positive for the Gibbs case.
Original publication:
Jörn Dunkel & Stefan Hilbert,
"Consistent thermostatistics forbids negative absolute temperatures",
Nature Physics (2013)
doi:10.1038/nphys2815
Published online, 8 December 2013
Contact:
Dr. Stefan Hilbert
MaxPlanckInstitut für Astrophysik
Tel: +49 (89) 30 000 2249
Email: shilbertmpagarching.mpg.de
Dr. Hannelore Hämmerle
Presse und Öffentlichkeitsarbeit
MaxPlanckInstitut für Astrophysik
Tel: +49 (89) 30 000 3980
Email: prmpagarching.mpg.de
