Blundell Thermal Physics · Problem 19.6

Equipartition of energy

Physics — Statistical Mechanics · equipartition-non-quadratic-power-law

Problem

If the energy

E

of a system behaves like

E = \alpha|x|^n

, where

n = 1, 2, 3\ldots

and

\alpha > 0

, show that the average energy is

\langle E \rangle = \xi k_\mathrm{B}T

, where

\xi

is a numerical constant.