Spatial distribution of thermal energy in equilibrium

Yohai Bar-Sinai, Eran Bouchbinder

Research output: Contribution to journalArticlepeer-review


The equipartition theorem states that in equilibrium, thermal energy is equally distributed among uncoupled degrees of freedom that 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 or disordered systems. Here we show that for systems undergoing simple Gaussian fluctuations around an equilibrium state, the spatial distribution is universally bounded from above by 12kBT. We further 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 and that in higher dimensions nontrivial spatial distributions emerge. Some implications are discussed.

Original languageEnglish
Article number060103
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
StatePublished - 9 Jun 2015
Externally publishedYes


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