Editing Debye model (section)

== Extension to liquids ==

It was long thought that phonon theory is not able to explain the heat capacity of liquids, since liquids only sustain longitudinal, but not transverse phonons, which in solids are responsible for 2/3 of the heat capacity. However, [[Brillouin scattering]] experiments [[neutron scattering|with neutrons]] and [[X-ray scattering|with X-rays]], confirming an intuition of [[Yakov Frenkel]],<ref>In his textbook ''Kinetic Theory of Liquids'' (engl. 1947)</ref> have shown that transverse phonons do exist in liquids, albeit restricted to frequencies above a threshold called the Frenkel frequency. Since most energy is contained in these high-frequency modes, a simple modification of the Debye model is sufficient to yield a good approximation to experimental heat capacities of simple liquids.<ref>{{cite journal |last1=Bolmatov |first1=D. |last2=Brazhkin |first2=V. V. |last3=Trachenko |first3=K. |title=The phonon theory of liquid thermodynamics |journal=Scientific Reports |date=2012 |volume=2 |page=421 |doi=10.1038/srep00421|pmid=22639729 | pmc=3359528 |arxiv=1202.0459 |bibcode=2012NatSR...2..421B }}</ref> More recently, it has been shown that instantaneous normal modes associated with relaxations from saddle points in the liquid energy landscape, which dominate the frequency spectrum of liquids at low frequencies, may determine the specific heat of liquids as a function of temperature over a broad range.<ref>{{cite journal |last1=Baggioli |first1=M. |last2=Zaccone |first2=A. |title=Explaining the specific heat of liquids based on instantaneous normal modes |journal=Physical Review E |date=2021 |volume=104 |issue=1 |page=014103 |doi=10.1103/PhysRevE.104.014103 |pmid=34412350 |arxiv=2101.07585 |bibcode=2021PhRvE.104a4103B }}</ref>