{"query": "The second law — entropy increases, the arrow, the one end", "count": 20, "results": [{"id": "card_thermo_second_law", "title": "The second law — entropy increases, the arrow, the one end", "shelf": "codex", "surface": "secular", "snippet": "Entropy of an isolated system never decreases. The microscopic laws are time-reversible; this is where irreversibility enters - the arrow of time. Of the vast many microstates almost all flow to the o", "authority_tier": "engine_derived", "source": "Narrow Highway — thermodynamics", "readable": false, "generated": false}, {"id": "card_theory_second_law_of_thermodynamics", "title": "Second law of thermodynamics (entropy)", "shelf": "theories", "surface": "secular", "snippet": "Second law of thermodynamics (entropy) — an engine domain that can touch it: thermodynamics. Calibration: partial — efficiency and entropy changes compute; the arrow of time is map-only. The entropy o", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_statistical_mechanics", "title": "Statistical mechanics (Boltzmann — why the second law is a counting argument)", "shelf": "theories", "surface": "secular", "snippet": "Statistical mechanics (Boltzmann — why the second law is a counting argument) — an engine domain that can touch it: thermodynamics. Calibration: seals — Boltzmann distributions, partition functions an", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_shannon_information_theory", "title": "Shannon information theory (entropy, channel capacity)", "shelf": "theories", "surface": "secular", "snippet": "Shannon information theory (entropy, channel capacity) — an engine domain that can touch it: information_theory. Calibration: seals. H = -Σ p log p. Information is measured by how much UNCERTAINTY a m", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_landauer", "title": "Landauer's principle (erasing information costs heat)", "shelf": "theories", "surface": "secular", "snippet": "Landauer's principle (erasing information costs heat) — an engine domain that can touch it: information_theory. Calibration: seals — the energy bound computes exactly. ERASING one bit must dissipate a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_category_theory", "title": "Category theory (the mathematics of structure-preserving maps)", "shelf": "theories", "surface": "secular", "snippet": "Category theory (the mathematics of structure-preserving maps) — an engine domain that can touch it: mathematics. Calibration: map-only — an organising framework rather than a computation. Study objec", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_carnot_efficiency", "title": "The Carnot limit (the ceiling on every engine ever built)", "shelf": "theories", "surface": "secular", "snippet": "The Carnot limit (the ceiling on every engine ever built) — an engine domain that can touch it: thermodynamics. Calibration: seals — the efficiency bound computes from two temperatures. No heat engine", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_third_law_of_thermodynamics", "title": "Third law of thermodynamics", "shelf": "theories", "surface": "secular", "snippet": "Third law of thermodynamics — an engine domain that can touch it: thermodynamics. Calibration: map-only — a limiting statement, not a computation. As temperature approaches absolute zero, the entropy ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_quantum_information___entanglement__von_neumann_entr", "title": "Quantum information & entanglement (von Neumann entropy)", "shelf": "theories", "surface": "secular", "snippet": "Quantum information & entanglement (von Neumann entropy) — an engine domain that can touch it: information_theory. Calibration: seals. S = -Tr(ρ log ρ), the entropy of a density matrix, which reduces ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_holographic_principle", "title": "The holographic principle & black-hole entropy", "shelf": "theories", "surface": "secular", "snippet": "The holographic principle & black-hole entropy — an engine domain that can touch it: physics. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RESONANCE). Th", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_free_energy_principle", "title": "The free-energy principle (Friston)", "shelf": "theories", "surface": "secular", "snippet": "The free-energy principle (Friston) — an engine domain that can touch it: medicine. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RESONANCE). Living syste", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_sys_entropy_arrow", "title": "The arrow of time — the root of every one-way form", "shelf": "systems", "surface": "secular", "snippet": "Why can any path run one way and not the other? Because the world itself does. The second law of thermodynamics: in an isolated system entropy does not spontaneously decrease (dS ≥ 0) — heat flows hot", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "readable": false, "generated": false}, {"id": "card_bridge_theory_statistical_mechanics__shannon_information_theory", "title": "Bridge: Statistical mechanics (Boltzmann — why the second law is a counting argument)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Statistical mechanics (Boltzmann — why the second law is a counting argument) and Shannon information theory (entropy, channel capacity) are the same form in different domains. Boltzmann's log W and S", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_alm_connection_entropy_is_thermodynamic", "title": "Almanac: Shannon entropy and thermodynamic entropy are the same quantity", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  The entropy of a message and the entropy of a gas are not analogies -- they are one formula. information_theory confirmed Shannon entropy numerically: a fair coin carries 1 bit, four equal", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_bridge_theory_landauer__shannon_information_theory", "title": "Bridge: Landauer's principle (erasing information costs heat)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Landauer's principle (erasing information costs heat) and Shannon information theory (entropy, channel capacity) are the same form in different domains. THIS CLOSES THE INFORMATION-THERMODYNAMICS BRID", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_shannon_information_theory__second_law_of_thermodynamics", "title": "Bridge: Shannon information theory (entropy, channel capacity)  ↔  Second law of thermodynamics (entropy)", "shelf": "bridges", "surface": "secular", "snippet": "Shannon information theory (entropy, channel capacity) and Second law of thermodynamics (entropy) are the same form in different domains. Shannon's H = -sum p log p and Boltzmann's S = k log W are the", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_quantum_information___entanglement__von_neumann_entr__shannon_information_theory", "title": "Bridge: Quantum information & entanglement (von Neumann entropy)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Quantum information & entanglement (von Neumann entropy) and Shannon information theory (entropy, channel capacity) are the same form in different domains. von Neumann entropy S = -Tr(rho log rho) red", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_category_theory__group_theory", "title": "Bridge: Category theory (the mathematics of structure-preserving maps)  ↔  Group theory & symmetry (the mathematics of what stays the same)", "shelf": "bridges", "surface": "secular", "snippet": "Category theory (the mathematics of structure-preserving maps) and Group theory & symmetry (the mathematics of what stays the same) are the same form in different domains. a group IS a category with o", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_logarithm", "title": "The logarithm - the instrument the joints share", "shelf": "codex", "surface": "secular", "snippet": "Two trees: Napier's table (1614) and Saint-Vincent's hyperbola (1647) - a number's logarithm as a tabulated count, and as an area. They become one function in Euler's Introductio (1748): e, and exp an", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_sys_thermal", "title": "Thermal systems", "shelf": "systems", "surface": "secular", "snippet": "Effort = temperature, flow = heat flow. Thermal resistance (Fourier: q = ΔT/R), thermal capacitance (a body's heat storage); no true thermal inductor (heat has no inertia) — the one place the analogy ", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_thermo_second_law"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}