TY - GEN A1 - Hartmann, Carsten A1 - Schütte, Christof T1 - A geometric approach to free energy calculations N2 - We consider a particle constrained to a submanifold ? of the configuration space Rm. Using that the notion of holonomic constraints coincides with integrability of the corresponding vector field, we show how this property naturally determines local coordinates on ?. We give a rigorous justification for the calculation of the mean force along a constrained coordinate, and we provide a concise geometrical interpretation of the different contributions to the mean force in terms of the unconstrained vector field and extrinsic curvature properties of ? in Rm. Our approach gives rise to a Hybrid Monte-Carlo based algorithm that can be used to compute the mean force acting on selected coordinates in the context of thermodynamic free energy statistics. Y1 - 2004 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/82 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-827 ER -