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We consider the problem of time-stepping/sampling for molecular and meso-scale particle dynamics. The aim of the work is to derive numerical time-stepping methods that generate samples exactly from the desired target temperature distribution. The numerical methods proposed in this paper rely on the well-known splitting of stochastic thermostat equations into conservative and fluctuation-dissipation parts. We propose a methodology to derive numerical approximation to the fluctuation-dissipationdoi:10.1016/j.procs.2011.04.146 fatcat:3ece7ne56vgvbafrsvgpvexqge