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Negative temperatures that are hotter than the Sun
Since middle school, science teachers drill into students the idea that nothing can ever be colder than absolute zero, or 0 Kelvin. On the Kelvin scale, everything has a positive temperature.
A group of scientists at the University of Munich in Germany, however, have cajoled some atoms into having negative temperatures on the Kelvin scale. To understand how this is possible, one must reconsider the definition of temperature.
The commonplace definition relates the kinetic energy of the atoms in a system to the system’s temperature. The lower average kinetic energy, the lower the temperature. At absolute zero, the atoms have no kinetic energy whatsoever.
However, the more rigorous thermodynamic definition of temperature relates it to the distribution of energy states of the atoms in the system and the system’s entropy. For positive temperatures, there is an absolute minimum energy that atoms can have. At positive temperatures, most atoms have a fairly low energy close to the minimum, with a few atoms occupying higher energy states. As more energy is pumped into the system, more and more atoms begin to move to higher energy states. The entropy of the system increases, as atoms begin to occupy more energy states.
Negative temperatures, on the other hand, are the total opposite. Instead of an absolute minimum, there is an absolute maximum energy that atoms can have. In a negative temperature system, most atoms occupy high energy states, with only a few atoms at lower energies. As more energy is pumped into such a system, more atoms move to the absolute maximum energy state. Since more atoms share the same state, the entropy of the system actually decreases with increasing energy.
To create the negative temperature, the scientists suspended about 100,000 potassium atoms in a lattice using lasers, cooling them down to a few billionths Kelvin above zero. Normally, the atoms repel each other. A sudden change in the magnetic field surrounding the lattice, however, caused the atoms to attract each other, creating a negative pressure. What keeps the atoms from collapsing is their sudden transition from their low-energy state to the highest possible energy state. For a few hundred milliseconds, the scientists had a cloud of potassium atoms at a few billionths Kelvin below absolute zero.
It is important to note that negative temperatures do not mean the atoms are somehow colder than absolute zero. In fact, the researchers say they are hotter than infinity. The atoms were not gradually cooled past zero, but rather jumped instantaneously from positive to negative temperatures.
The researchers note that negative energies may have some interesting implications. Because negative temperature systems are hotter than positive temperature systems, heat would flow from negative to positive systems, leading to heat engines with efficiencies greater than 100%. The relationship between entropy and negative temperature implies that at maximum entropy temperature may become discontinuous as it jumps from positive to negative.
Negative temperatures may also help astronomers. The negative pressure experienced by the atoms is also seen on the cosmological scale as the mysterious dark energy that binds the universe together. The scientists suggest that experimenting with such negative temperature systems may help unlock one of the greatest mysteries of the universe.