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For an ideal gas,
it is proportional to the kinetic energy of its constituent particles. In
general, it is described as connected to the internal energy of the system.
Measuring the temperature is done macroscopically by thermometers – two bodies
in contact will reach over time the same temperature. Doing that in the quantum
world is not as straightforward. Energy cannot be known with arbitrary
precision, due to the Heisenberg uncertainty principle.

You either isolate
the object completely to establish its energy or you use a thermometer that
will influence your system. There’s no winning if you want to measure the
quantum temperature. A recent study in Nature Communications describes
a generalized version of the energy-temperature uncertainty relation, which
remains valid for both quantum and classical systems alike.

The temperature
has a certain uncertainty that can’t be reduced, but this allows us to take it
into account. One issue, in particular, is the superposition of the energy
states. The concept of superposition has been made famous by physicist Erwin
SchrÃ¶dinger. In his thought experiment, a cat is trapped in a box with a vial
of poison that can be activated by a quantum process.

Since the
scientist doesn’t know what’s happening in there, the cat is both alive and
dead – it exists in two states at the same time. For the thermometer, this
happens for temperature states. The findings are important for the design
of optimal nanoscale thermometers. These might not be useful in everyday life,
but they will play a pivotal role in the successful functioning of many
upcoming technologies.

“In the quantum case, a quantum thermometer... will be in a superposition of energy states simultaneously,” author Harry Miller, from the University of Exeter, told Live Science. “What we find is that because the thermometer no longer has a well-defined energy and is actually in a combination of different states at once, that this actually contributes to the uncertainty in the temperature that we can measure.”

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