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the claim
The equipartition theorem applies differently to vibrational modes at various temperatures
the verdict
COMMON KNOWLEDGE
no citation needed for this one
refutedsupported
the weight of evidence
no sources on either side

The breakdown of the equipartition theorem at low temperatures due to quantum freeze-out of vibrational modes is a foundational concept in statistical mechanics and thermodynamics, requiring no citation.

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The analysis

The claim refers to the standard quantum mechanical modification of the equipartition theorem, where high-frequency vibrational modes freeze out at lower temperatures (contributing less than $k_BT$ per degree of freedom). This is a textbook piece of common knowledge in physics, rendering specific source citation unnecessary.

Everything we examined (12)
  1. Temperature dependence of hydrogen vibrational modes in passivated boron-doped siliconpeer-reviewedno side takennot shown: read and judged not to bear on this claim
  2. On the Temperature Dependence of Infrared Absorption Lines due to Lattice Vibrational Modespeer-reviewedno side takennot shown: read and judged not to bear on this claim
  3. Consequences of the failure of equipartition for the <i>p</i>-<i>V</i> behavior of liquid water and the hydration free energy components of a small protein.peer-reviewedno side takennot shown: read and judged not to bear on this claim
  4. The CP2K Program Package Made Simple.peer-reviewedno side takennot shown: read and judged not to bear on this claim
  5. Role of Structural Changes at Vitrification and Glass-Liquid Transition.peer-reviewedno side takennot shown: read and judged not to bear on this claim
  6. Scalable machine learning approach to light induced order disorder phase transitions with ab initio accuracy.peer-reviewedno side takennot shown: read and judged not to bear on this claim
  7. Density functional theory study of mechanical, thermal, and thermodynamic properties of zinc-blende CdS and CdSe.peer-reviewedno side takennot shown: read and judged not to bear on this claim
  8. Study on the Molecular Dynamics of 2‑(4-Fluorophenyl)-6-methyl-4-(3- (trifluoromethyl)phenyl)-1,2-dihydrodipyrazolo[3,4-b:3',4'‑<i>d</i>]pyridin-3(6<i>H</i>)‑one for Cancer Immunotherapy Using a Dpeer-reviewedno side takennot shown: read and judged not to bear on this claim
  9. Vibrational Partition Functions from Bond Order and Populations Relationships.peer-reviewedno side takennot shown: read and judged not to bear on this claim
  10. Ferrite Nanocubes Coupled with Gold Nanorods: A Plasmonic Leap in Hyperthermia Efficiency.peer-reviewedno side takennot shown: read and judged not to bear on this claim
  11. Quasiballistic thermal transport in submicron-scale graphene nanoribbons at room-temperature.peer-reviewedno side takennot shown: read and judged not to bear on this claim
  12. Comprehensive Modeling of Acetone Clusters: QTAIM Analysis and QCE Study.peer-reviewedno side takennot shown: read and judged not to bear on this claim
The paper trail · every fact has a biography
first checked05 Aug 2026
judged → COMMON KNOWLEDGE · 9505 Aug 2026
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