Thermostat algorithm for generating target ensembles

We present a deterministic algorithm called contact density dynamics that generates any prescribed target distribution in the physical phase space. Akin to the famous model of Nosé and Hoover, our algorithm is based on a non-Hamiltonian system in an extended phase space. However, the equations of motion in our case follow from contact geometry and we show that in general they have a similar form to those of the so-called density dynamics algorithm. As a prototypical example, we apply our algorithm to produce a Gibbs canonical distribution for a one-dimensional harmonic oscillator.