{"query": "Fokker–Planck", "count": 14, "results": [{"id": "card_n_041763374eca", "title": "Fokker–Planck & Liouville — probability flow in statistical mechanics", "shelf": "science", "surface": "secular", "snippet": "The stochastic instantiation of probability-as-fluid. Fokker–Planck sets the current\nJ = μρ − D∇ρ (drift + diffusion); its steady state is the Boltzmann distribution ρ ∝ e^(−U/kT),\nwhich makes the cur", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_n_8530c72a2201", "title": "Fluid probability dynamics — one continuity equation across physics, geometry, and ML", "shelf": "science", "surface": "secular", "snippet": "One equation wears many clothes. Probability is a conserved fluid: the continuity equation\ndρ/dt + ∇·J = 0 (current J = ρv) says density is never created or destroyed — it only flows. The\nsame skeleto", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_c_ec9bfe0734fd", "title": "Gibbs free energy — will a reaction go? ↔ Fokker–Planck & Liouville — probability flow", "shelf": "connections", "surface": null, "snippet": "This is the second law of thermodynamics doing chemistry, the same entropy arrow that pointed the Fokker–Planck fluid toward equilibrium.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_src_pron_fokkers", "title": "fokkers", "shelf": "pronunciation", "surface": "secular", "snippet": "fokkers: pronounced (ARPABET) F AA1 K ER0 Z. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "generated": false}, {"id": "card_src_pron_fokker", "title": "fokker", "shelf": "pronunciation", "surface": "secular", "snippet": "fokker: pronounced (ARPABET) F AA1 K ER0. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "generated": false}, {"id": "card_src_book_68381", "title": "Heilige Banden: Roman — Abraham Anthony Fokker", "shelf": "gutenberg", "surface": "secular", "snippet": "Heilige Banden: Roman, by Abraham Anthony Fokker (in nl). Subjects: Indonesia -- Fiction. Read the full text (public domain): https://www.gutenberg.org/ebooks/68381", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_book_67653", "title": "Om het recht der liefde — Abraham Anthony Fokker", "shelf": "gutenberg", "surface": "secular", "snippet": "Om het recht der liefde, by Abraham Anthony Fokker (in nl). Subjects: Indonesia -- Fiction. Read the full text (public domain): https://www.gutenberg.org/ebooks/67653", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_book_65698", "title": "Maleisch-Nederlandsche Gesprekken — Abraham Anthony Fokker", "shelf": "gutenberg", "surface": "secular", "snippet": "Maleisch-Nederlandsche Gesprekken, by Abraham Anthony Fokker (in nl). Subjects: Indonesian language -- Conversation and phrase books -- Dutch. Read the full text (public domain): https://www.gutenberg", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_c_e655b3fcef54", "title": "Optimal transport instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "The geometry of moving probability — Fokker–Planck as a Wasserstein gradient flow.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_c_3cc9f3e8e74f", "title": "Fokker–Planck & Liouville instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "Statistical mechanics is the stochastic instance of the probability-continuity equation.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_c_c1d4f07c75cd", "title": "Fokker–Planck & Liouville — probability flow ↔ Fluid probability dynamics — one continuity ", "shelf": "connections", "surface": null, "snippet": "The stochastic instantiation of probability-as-fluid. ... In Hamiltonian phase space, Liouville's theorem gives dρ/dt = 0 — the probability fluid is incompressible.  — a concord the card itself states", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_c_583b49254af6", "title": "Fluid probability dynamics — one continuity  ↔ Optimal transport — the geometry of moving p", "shelf": "connections", "surface": null, "snippet": "geometry (optimal transport: distance = least kinetic energy to carry one distribution to another; Fokker–Planck is the gradient flow of free energy in Wasserstein space)  — a concord the card itself ", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_n_d59ca677ea24", "title": "Optimal transport — the geometry of moving probability", "shelf": "science", "surface": "secular", "snippet": "Benamou–Brenier: the distance between two distributions is the least kinetic energy of a\nfluid that carries one to the other, subject to the continuity equation. Jordan–Kinderlehrer–Otto\n(1998): the F", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "generated": false}, {"id": "card_n_de34fa421022", "title": "Gibbs free energy — will a reaction go?", "shelf": "science", "surface": "secular", "snippet": "ΔG = ΔH − T·ΔS decides spontaneity: a reaction proceeds on its own only when ΔG < 0.\nSealed in-domain: ΔH = −100 kJ/mol, ΔS = 200 J/mol·K at 300 K gives ΔG = −160 kJ/mol —\nspontaneous (https://narrowh", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}]}