Generation of arbitrary probability distributions from chaotic dynamics

A framework is developed to derive nonlinear dynamical systems that chaotically generate arbitrary multivariate probability distributions with smooth, deterministic trajectories. The ideas are used to extend the Nose-Hoover thermostat methodology to three-dimensional cases where the momentum distribution is nonisotropic and/or non-Gaussian. Toy models that generate several well-known distributions in physics are given as pedagogical examples.