In his later years, his work concentrated on the fundamental role of indeterminism in nonlinear systems on both the classical and quantum level. Prigogine and coworkers proposed a Liouville space extension of quantum mechanics. A Liouville space is the vector space formed by the set of (self-adjoint) linear operators, equipped with an inner product, that act on a Hilbert space. There exists a mapping of each linear operator into Liouville space, yet not every self-adjoint operator of Liouville space has a counterpart in Hilbert space, and in this sense Liouville space has a richer structure than Hilbert space. The Liouville space extension proposal by Prigogine and co-workers aimed to solve the arrow of time problem of thermodynamics and the measurement problem of quantum mechanics.