Negative temperature
Certain thermodynamic systems can achieve negative thermodynamic temperature; that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This should be distinguished from temperatures expressed as negative numbers on non-thermodynamic Celsius or Fahrenheit scales, which are nevertheless higher than absolute zero.
Temperature is related to how particles are distributed among the available energy states of a system. At ordinary positive temperatures, lower-energy states are more likely to be occupied than higher-energy states. At negative temperatures, this distribution is reversed, so higher-energy states become more populated than lower-energy ones. For this reason, a system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system. A standard example of such a system is population inversion in laser physics.
Temperature is also related to how a system's entropy changes as energy is added. Thermodynamic systems with no upper limit on their energy cannot achieve negative temperatures. This is the case for ordinary particles, such as atoms or dust, whose kinetic energy can increase without bound. In such systems, adding energy always increases the number of accessible states and therefore the entropy. Negative temperatures are only possible in systems that have a maximum energy they can hold. As such systems approach this maximum energy, the number of accessible states begins to decrease with further increases in energy, causing the entropy to fall and making the temperature negative. Examples of such systems include two-level systems and nuclear spin ensembles in an external magnetic field.