  The nested sampling algorithm has been shown to be a general method for
calculating the pressure-temperature-composition phase diagrams of materials.
While the previous implementation used single-particle Monte Carlo moves, these
are inefficient for condensed systems with general interactions where
single-particle moves cannot be evaluated faster than the energy of the whole
system. Here we enhance the method by using all-particle moves: either Galilean
Monte Carlo or a total enthalpy Hamiltonian Monte Carlo algorithm, introduced
in this paper. We show that these algorithms enable the determination of phase
transition temperatures with equivalent accuracy to the previous method at
$1/N$ of the cost for an $N$-particle system with general interactions, or at
equal cost when single particle moves can be done in $1/N$ of the cost of a
full $N$-particle energy evaluation.
