Information geometry of perturbed gradient flow systems on hypergraphs: A perspective towards nonequilibrium physics

arXiv:2510.27268 · cond-mat.stat-mech, math.DG, math.DS, physics.chem-ph, q-bio.MN · Submitted 2025-10-31 · Read on arXiv

cond-mat.stat-mech, math.DG, math.DS, physics.chem-ph, q-bio.MN

Submitted: 2025-10-31

Updated: 2026-09-22

Terminology

• Gradient Flow — 86× in this paper · explained in 2 episodes
• Hypergraph — 28× in this paper · explained in 2 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Lyapunov function — 3× in this paper · explained in 2 episodes
• Optimal Transport — 3× in this paper · explained in 5 episodes
• Boltzmann Equation — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Fluctuation theorems with optical tweezers: theory and practice
• Information geometry of excess and housekeeping entropy production
• The Geometry of Thermodynamic Uncertainty Relations in Chemical Reaction Networks
• Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow
• An Eulerian formulation for dissipative materials using Lie derivatives and GENERIC
• Information geometry of chemical reaction networks: Cramer-Rao bound and absolute sensitivity revisited

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