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Within the post Newtonian framework the fully reduced Hamiltonian (i.e., witheliminated spin supplementary condition) for the next-to-leading orderspin-squared dynamics of general compact binaries is presented. The Hamiltonianis applicable to the spin dynamics of all kinds of binaries withself-gravitating components like black holes and/or neutron stars taking intoaccount spin-induced quadrupolar deformation effects in second post-Newtonianorder perturbation theory of Einstein's field equations. The correspondingequations of motion for spin, position and momentum variables are given interms of canonical Poisson brackets. Comparison with a nonreduced potentialcalculated within the Effective Field Theory approach is made.

Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries