Narrative Realities and Optimal Entropy

Estimation Entropy and Optimal Observability

We consider a pair of correlated processes {Zn}n=−∞ and {Sn}n=−∞, where the former is observable and the latter is hidden. The uncertainty in the estimation of Sn upon the finite past history of Zn−1 0 is H(Sn|Z n−1 0 ) which is a sequence of n. The limit of Cesaro mean of this sequence is called the estimation entropy. We show that the estimation entropy is the long run average entropy of the ...

Ricci Flow , Entropy and Optimal Transportation ∗

Let a smooth family of Riemannian metrics g(τ) satisfy the backwards Ricci flow equation on a compact oriented n-dimensional manifold M . Suppose two families of normalized n-forms ω(τ) ≥ 0 and ω̃(τ) ≥ 0 satisfy the forwards (in τ) heat equation on M generated by the connection Laplacian ∆g(τ). If these n-forms represent two evolving distributions of particles over M , the minimum root-mean-squa...

Ricci curvature, entropy and optimal transport

This is the lecture notes on the interplay between optimal transport and Riemannian geometry. On a Riemannian manifold, the convexity of entropy along optimal transport in the space of probability measures characterizes lower bounds of the Ricci curvature. We then discuss geometric properties of general metric measure spaces satisfying this convexity condition. Mathematics Subject Classificatio...

Comparison of entropy generation minimization principle and entransy theory in optimal design of thermal systems

In this study, the relationship among the concepts of entropy generation rate, entransy theory, and generalized thermal resistance to the optimal design of thermal systems is discussed. The equations of entropy and entransy rates are compared and their implications for optimization of conductive heat transfer are analyzed. The theoretical analyses show that based on entropy generation minimizat...

Dollarization: Myths and Realities