# Temperature Less Than Nothing? [duplicate]

How temperature can be less than nothing or less than absolute zero?And how atoms interact in this level?

## marked as duplicate by Aaron Stevens, user191954, Cosmas Zachos, Community♦Mar 8 at 16:02

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## 1 Answer

See here for an overview, but it helps to define temperature from a statistical mechanics approach. Specifically, we define temperature as the change in energy caused by a change in entropy. A more intuitive approach is to consider inverse temperature, also known as coldness or thermodynamic beta, which is defined as the change in entropy (extent of mixing/randomness) induced by a given change in energy. Note that, although it's the inverse of temperature, thermodynamic beta is negative if and only if temperature is negative. So, we can look at the beta of systems, and if it is negative, temperature will be as well.

Now, consider a system in which, when I apply more energy to it, the entropy decreases. Lasers are a good example of this: by exciting many electrons from the ground state to the 1st excited state, I've actually made a population inversion. In doing so, when I excite electrons to the excited state, the order of mixing (entropy) decreases as the majority of the electrons were already in the excited state. Thus the input of energy to the system lowered the entropy, resulting in a negative thermodynamic beta (and therefore temperature).