From the 1 of 4 linked papers with an AI index.
4 papers
Spending Operators and Weak Power-Port Decompositions for Path-Dependent Entropic Lagrangians
Huilong Ren
The paper develops a mathematical framework for path‑dependent entropic Lagrangians, introducing spending operators and a weak power‑port decomposition that handle channelwise term…
Path-Dependent Entropic Lagrangian for Probability Flows: Balance--Entropy Routing and Composable Information Potentials
Huilong Ren
Probability distributions are central to information theory, statistical inference, and modern probabilistic learning. Maximum entropy selects a probability state under prescribed…
Path-Dependent Energy Lagrangian for Irreversible Thermomechanical Systems
Huilong Ren
We present a minimal Path-Dependent Energy Lagrangian (PDEL) that generates, from a single action, the balance equations of mechanics and the entropy/heat equation for irreversible…
CDF-Generated Damage Laws: Admissibility, Gamma-Convergence to Griffith Fracture, and Well-Posedness
Huilong Ren
We formulate a family of scalar softening laws by setting the stored-energy density , where ranges over exponential, Cauchy, logistic, half-norma…