The KAM theory can be used to show that this theorem does not hold for a sufficiently small perturbation of an integrablesys
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