The Connection between Information Geometry and Geometric Mechanics
نویسندگان
چکیده
Abstract: The divergence function in information geometry, and the discrete Lagrangian in discrete 1 geometric mechanics each induce a differential geometric structure on the product manifold QˆQ. 2 We aim to investigate the relationship between these two objects, and the fundamental role that 3 duality, in the form of Legendre transforms, play in both fields. By establishing an analogy between 4 these two approaches, we will show how a fruitful cross-fertilization of techniques arise. In particular, 5 we establish, through variational error analysis that the divergence function agrees with exact discrete 6 Lagrangian up to third order if and only if Q is a Hessian manifold. 7
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