The KAM theory can be used to show that this theorem does not hold for a sufficiently small perturbation of an integrablesystem because the KAM tori survive; if the perturbation is large enough, the tori do not survive and this theorem holds. TheFermi-Pasta-Ulam experiment discovered that this theorem failed to hold for the coupled anharmonic spring system, becausethe qua
The KAM theory can be used to show that this theorem does not hold for a sufficiently small perturbation of an integrablesystem because the KAM tori survive; if the perturbation is large enough, the tori do not survive and this theorem holds. TheFermi-Pasta-Ulam experiment discovered that this theorem failed to hold for the coupled anharmonic spring system, becausethe quantity of interest was shared between only a few modes of the system. This theorem is only assured to hold under theassumption that the ergodic hypothesis is true. One consequence of this theorem is that a purely classical ideal gas must havea constant speciÂfic heat, because an alternative formulation of this theorem is that each quadratic term in its energy functioncontributes one-half times the Boltzmann constant to the specifiÂc heat. For 10 points, identify this theorem of thermodynamicsaccording to which, at equilibrium, each degree of freedom of a particle contributes one-half times Boltzmann's constant timestemperature to its energy.
The KAM theory can be used to show that this theorem does not hold for a sufficiently small perturbation of an integrablesystem because the KAM tori survive; if the perturbation is large enough, the tori do not survive and this theorem holds.
equipartition theorem