  This article presents a new numerical scheme for the discretization of
dissipative particle dynamics with conserved energy. The key idea is to reduce
elementary pairwise stochastic dynamics (either fluctuation/dissipation or
thermal conduction) to effective single-variable dynamics, and to approximate
the solution of these dynamics with one step of a Metropolis-Hastings
algorithm. This ensures by construction that no negative internal energies are
encountered during the simulation, and hence allows to increase the admissible
timesteps to integrate the dynamics, even for systems with small heat
capacities. Stability is only limited by the Hamiltonian part of the dynamics,
which suggests resorting to multiple timestep strategies where the stochastic
part is integrated less frequently than the Hamiltonian one.
