Abstract
Recent results about the supersymmetries of random systems governed by stochastic differential equations have classical analogues in terms of geometrical symmetries in the configuration space of commuting variables. The related results are: (1) the reversible drift velocity of a stationary stochastic process is a Killing vector of the diffusion metric; (2) the irreversible drift velocity is a geodesic tangent vector; (3) the stationary current conservation equation is a special case of the general result that scalar products of Killing vectors with geodesic tangent vectors are constants of the motion. The physical postulate is that microscopic reversibility is to the normality of time translation generators what time reversal invariance is to the hermiticity of hamiltonians.
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