2026/01/31 by Anonymous, Jordan R Sawchuk, David A Sivak
Computer Science · Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Contact Mechanics and Variational Inequalities #Control and Stability of Dynamical Systems #cond-mat.stat-mech
paper · pdf · doi:10.1103/bhr1-lplt
6 pages, 2 figures, 5 appendices
openalex publication_date 2026/07/08 · openalex created_date 2026/07/09 · openalex updated_date 2026/07/09 · arxiv created 2026/07/30 · arxiv updated 2026/07/31
We demonstrate that the thermodynamic friction metric governing dissipation in slowly driven continuous-time Markov chains is equivalent to the commute-time embedding and the resistance distance. This equivalence yields complementary insights: The commute-time embedding demonstrates the intrinsic cost of transporting probability across dynamical bottlenecks, while the resistance distance maps thermodynamic dissipation to Joule heating in an electrical network. We further demonstrate that the linear-response thermodynamic distance is a discrete L2-Wasserstein optimal transport cost evaluated along paths of equilibrium distributions, extending a continuous-state correspondence to discrete networks. This conceptual synthesis of linear-response thermodynamics, random walks on graphs, electrical circuits, and optimal-transport theory connects independently developed geometric frameworks, reduces complex metric calculations to simple circuit algebra, and provides a clear physical picture of dissipation as the energetic cost of routing probability through the state space network.