In this case, the particle velocities are continuous and unbounded. The energy of the configuration is independent of the position of the particles, and is the sum of the kinetic energies of the individual particles. Hence, for and ideal gas, the only coordinates of interest are the velocities. In order to change a configuration, we choose a particle at random and change its velocity by a random amount. For simplicity we consider only the one-dimensional case.
We do not need to use the demon algorithm for an ideal gas, since a reduction in the energy of one particle can be easily compensated by the corresponding increase in the energy of another particle. However, in order to illustrate the more general case, we will use the demon anyway.