Gradient Structures from Classical to Quantum - Part 2 of 3

Explore the second part of a three-part lecture series on gradient structures presented by Oliver Tse from Eindhoven University of Technology at IPAM's Non-commutative Optimal Transport Tutorials. Delve into how gradient structures provide a framework for understanding dynamical systems through variational principles, connecting concepts across thermodynamics, optimal transport, and quantum mechanics. The lecture examines both classical gradient structures in dissipative systems and their quantum counterparts, highlighting applications in open quantum systems, entropy dissipation, and non-commutative transport. This 86-minute presentation, recorded on March 13, 2025, at UCLA's Institute for Pure & Applied Mathematics, bridges classical and quantum perspectives to reveal emerging mathematical structures that offer new insights into dynamics across both domains.