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In this paper we establish quantitative results about the bridges of theLangevin dynamics and the associated reciprocal processes. They include anequivalence between gradient estimates for bridge semigroups and couplings,comparison principles, bounds of the distance between bridges of differentLangevin dynamics, and a Logarithmic Sobolev inequality for bridge measures.The existence of an invariant measure for the bridges is also discussed andquantitative bounds for the convergence to the invariant measure are proved .All results are based on a seemingly new expression of the drift of a bridge interms of the reciprocal characteristic, which, roughly speaking, quantifies the" mean acceleration " of a bridge.

Couplings, gradient estimates and logarithmic Sobolev inequality for Langevin bridges