Spatial distribution of thermal energy in equilibrium. Bar-Sinai, Y. & Bouchbinder, E. *Phys. Rev. E Stat. Nonlin. Soft Matter Phys.*, 91(6):060103, June, 2015. abstract bibtex 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 1/2k(B)T. 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.

@ARTICLE{Bar-Sinai2015-wm,
title = "Spatial distribution of thermal energy in equilibrium",
author = "Bar-Sinai, Yohai and Bouchbinder, Eran",
abstract = "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 1/2k(B)T. 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.",
journal = "Phys. Rev. E Stat. Nonlin. Soft Matter Phys.",
volume = 91,
number = 6,
pages = "060103",
month = jun,
year = 2015,
language = "en"
}

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