Paper
Geometric calculations on probability manifolds from reciprocal relations in Master equations
Authors
Wuchen Li
Abstract
Onsager reciprocal relations model physical irreversible processes from complex systems. Recently, it has been shown that Onsager principles for master equations on finite states introduce a class of Riemannian metrics in a probability simplex, named probability manifolds. We call these manifolds finite-state generalized Wasserstein- spaces. In this paper, we study geometric calculations on probability manifolds, in which we derive the Levi-Civita connection, gradient, Hessian, and parallel transport, and compute the Riemannian and sectional curvatures. We present two examples of geometric quantities in probability manifolds. These include Levi-Civita connections from the chemical monomolecular triangle reaction and sectional, Ricci, and scalar curvatures in Wasserstein space on a three-point lattice.