On the spatial distribution of thermal energy in equilibrium

Yohai Bar-Sinai, Eran Bouchbinder

Published 2015-03-08Version 1

The equipartition theorem states that in equilibrium thermal energy is equally distributed among uncoupled degrees of freedom which appear quadratically in the system's Hamiltonian. However, for spatially coupled degrees of freedom --- such as interacting particles --- one may speculate that the spatial distribution of thermal energy may differ from the value predicted by equipartition, possibly quite substantially in strongly inhomogeneous/disordered systems. Here we show that in general the averaged thermal energy may indeed be inhomogeneously distributed, but is universally bounded from above by $\frac{1}{2}k_BT$. In addition, we show that in one-dimensional systems with short-range interactions, the thermal energy is equally partitioned even for coupled degrees of freedom in the thermodynamic limit.