1. A computer-implemented method of simulating behaviour of a thermodynamic system over time, the thermodynamic system having potential energy that can be split into more quickly varying parts and more slowly varying parts and having a state described by collective vectors of position and momentum at any given time, the method comprising a momentum refreshment process and a conservative dynamics process, wherein the momentum refreshment process comprises carrying out an operation of mixing the collective momentum vector with a noise vector and carrying out an acceptance/rejection operation; the conservative dynamics process comprises applying a multiple time stepping conservative dynamics operation to a current state, in which operation calculations for forces corresponding to more slowly varying energy parts in the thermodynamic system undergo an averaging procedure and are carried out at a larger time step than calculations for forces corresponding to more quickly varying energy parts; and carrying out an acceptance/rejection operation; wherein the acceptance/rejection operations are based on an approximation of the system energy expressed using shadow Hamiltonians and comprise accepting a current state or returning a replacement state.