Does anyone recognize this equation relating kT to mean squared displacement?

[kasse]

Does anyone recognize this equation?

$$\frac{k_BT}{2} = \alpha\frac{<x^2>}{2}$$

What does it describe?

 

[millitiz]

It look like something to do with Energy. Because the LHS has the unit of energy, while the RHS, hmm, looks a bit strange...

 

[CompuChip]

Doesn't it have to do with ideal gas in a box?

 

[Count Iblis]

It is the average potential energy of a harmonic oscillator in the high temperature limit.